I worked at a large insurance company, and my office environment is fun. Which probably isn't what you'd expect at a large insurance company, and indeed my previous team's office environment wasn't very fun, but my current one is.
Since 2/3 of the staff was laid off, you're at a significant disadvantage out of the gate. One of the top priorities (particularly for getting morale back up) should be making sure there are guarantees that there won't be further layoffs. Obviously this may not be in your control, but until there's a sense of stability I imagine good morale and a fun environment will be difficult to come by.
I largely agree with Vincour. The management in my area is a significant contributor to it being a fun environment. We have two de facto managers, with another one higher up who we see perhaps once a week. They practice what one of them called "servant leadership" - their main task is to make sure we can do our job and help remove obstacles, not to watch us 40 hours a week. We have a meeting each morning where we note what we did, and if we need help, whether from someone else on the team or from our "blocker remover" manager who plays the role of being the guy who lets other teams know "hey, we actually need this, Joe isn't just requesting it for fun". This both motivates us to not be in a position of "I twiddled my thumbs for 8 hours yesterday" while making sure we aren't twiddling our thumbs for 8 hours because of some other thing we couldn't fix. But anyway, this "blocker remover" manager is a sociable guy, joins us at happy hours, organizes team lunches every so often, and despite being sort-of-de-facto a manager, is as much a part of the team as anyone.
Our de jure manager works more with our business partners, but it's not uncommon for him (a former developer, a role that I and about half the other team members have) to come over and talk with the developers casually, sometimes about technical stuff but as often about his planned hunting expedition the next weekend, or the latest cats that he and his wife are fostering. It probably sounds almost too casual, but it means that everyone's comfortable talking with him, no one's on edge when he asks for a meeting with them, and he can bring up things he'd like us to work on as appropriate (although we're actually a pretty functional team, so those occurrences have been few and far between). It definitely helps that he used to be in our role, too, so he knows what it's like and that estimate are estimates. Basically, everyone's legitimately happy to see their manager.
Both managers are also very open with plans for the future. What projects we'll be working on next (either in a few weeks or next year), staffing plans for next year (in terms of number of positions by role, at a minimum), how the annual evaluation process works in significant detail, and so forth. It results in less uncertainty (which I'm sure will be appreciated after layoffs), and people liking to work with the managers.
As for environment, we talk with each other a fair amount, about both work-related and non-work-related topics. And the tone for talking about non-office-related things is set by management, and makes a huge difference in it being a fun environment versus a staid, quarantined-from-people-who-are-five-feet-a-way-from-you library type atmosphere. It ranges from the simple, "Anyone got any good plans for the weekend?" at our morning meeting on Fridays, to our "blocker remover" manager talking with people individually about casual topics if he and someone else are early to the meeting, to him occasionally staying late and discussing topics ranging from traveling to his daughter's post-college job prospects to how to improve our work environment with whoever is still there or is walking out with him, to our de jure manager wandering over after lunch to discuss guns for no specific reason. Since management is okay with discussing casual, not necessarily related to work at all things, other people feel comfortable talking with each other too, and this leads to an environment that is fun, and where people are comfortable talking with each other for any reason, which in turns helps productivity as well.
And this is important enough that it's worth calling out again - management should talk casually with people about various non-work related things, out of actual interest in their employees and the topics being discussed. Where management hasn't done this, I've been in quiet environments where I only get to know a few of my coworkers, and have little attachment to the company. Where they have - primarily this position - the work day is more enjoyable, I actually want to get up and go in to the office in the morning, and I know most of my coworkers fairly well (which also motivates me to stay with the company and team).
This also leads naturally to other fun events, some planned by management, but many not. We have team lunches or happy hours for things like birthdays, but most days there also is at least one group of team members who go out to lunch together. Occasionally we schedule a happy hour for no other reason than liking beer and liking hanging out with each other. There are various team jokes, traditions, and nicknames, all of which came up organically at some point or another. The traditions are optional, but tend to get fairly good participation. We revitalized an old one last month simply because a few of us were discussing it at lunch, said, "Why don't we start doing that again?", and sent out an invitation; one of the managers participated as well (and the other had been the inspiration). Occasionally we partake in various completely-outside-of-work events as a group, like going to an agricultural festival in a city near where one of our team members grew up after work one day in October. Again, the regular employee organized it, but one of our managers joined on the trip too, and we were happy to have him along.
Most other stuff is ancillary, though worth considering. We're flexible with people going to appointments - dentists', doctors', car service, etc. - so that doesn't stress anyone out. There's a ping-pong table a couple floors down (in its own room so it isn't a distraction), but only a couple people regularly play ping-pong, so it's only a minor part of the environment being fun. We occasionally go down to the local coffee shop as a group in the afternoon (for which being comfortable with each other is a prerequisite, and it's never planned in advance), but we occasionally share tea with each other too. Working from home when ill is encouraged (no one likes getting sick because someone else came in when sick), and is okay occasionally other times, but you are encouraged to come into the office whenever you aren't ill due to the benefits of the team atmosphere - and most people are happy to come in every day. No one cares if you take a reasonably-length break during the day to clear your mind, stretch your legs, call your dentist, etc. There's only one person on the team who's known for taking too long of breaks (i.e. disappearing for an hour or more multiple times a day), and everyone knows who that is, and it reflects on them. But generally, we trust each other. Sometimes people bring in treats to eat too, for no reason other than they feel like it, whether homemade baked goods, cookies from the store downstairs, or making waffles for the team for breakfast. It improves morale and makes work fun, but only works because we like each other.
By comparison, at a company I worked at previously, we had potlucks every so often, and people would bring food in. But there was no communal table to eat at, so everyone went back to their desks to eat, and since management was very quiet, most of the time people would just eat the potluck food silently while they resumed work, or at best talk about whatever they'd been working on that morning. The potluck was a good idea in theory but didn't really help make things fun in that environment.
If someone starts on the job and is a total flop, they don't stick around long. Which everyone's fine with because no one likes working with people who are bad at their job. We have 15-25 people (it varies a bit due to contractors); I joined in March and we've dismissed 3 contractors before the planned end of their contract since then (we'll also hire them outright if they're good enough). Yes, our interview process needs work, and that's a problem. But we don't keep the people who prove to be the wrong person around, and the team (and its morale) is better for that.
Having people who can lead in leadership positions is also crucial. Of the three main roles on my team, two of them have good leaders leading them, and one doesn't. Guess which one has the lowest morale and the most people talking about leaving? They've stuck around because they like the people on the team (fun atmosphere), and because there's been progress on addressing the leadership problem.
This may be more difficult with an existing environment and recent layoffs, but if the atmosphere can be made more friendly, open, and conversational, then I suspect you'll have progress over time, and happier and less-likely-to-leave employees as well.