Keeping Your Vassals Stable

I'm trying to get expand Russia to increase on the Soviet Empire

There's obviously a limit to how big you can expand even with Russia and 5* civics (police state, state property, occupation) enabled so I was planning to do this with Vassals.

I've already got a fairly large Persia (Soviet Gilan), Mongolia and Japan but Japan goes from stable to collapsing in about 3 turns, as does Mongolia. Other than liberating two cities on the Asian mainland which are Russian anyway (that's why I went to war with them) is there a way of stabilising them and stopping them from collapsing?

Gifting tech, resources etc? Would gifting them workers or settlers help, They have the Japanese mainland and Mindanao island (Davao and one other city). I thought that would be big enough for them.

I think I've stablilised Mongolia by giving them a couple of captured Chinese cities and liberating a few of their less productive cities but I'd rather find another way.

 

Remember the stability factors.
Expansion
Economy
Domestic
Foreign
Military
There are lots of way to help in the domestic area. For example, Civs with little resources often struggle to keep their citizens happy. This is all the more true for vassal with (+1 unhapiness: down with the foreign influence!). If you have surplus resources, gifting them some (or exchanging them for some of theirs) will help, as long as 1) You aren't causing more harm than good 2) You give them the kind of resource they need. Persia has a lot of spices, so getting some from them instead of building a city in some far away island with spices is a good way to make use of it:: if they need happiness you give them luxuries in exchange and kill two birds with one stone. Remember this may weaken your corporations, so be careful.
AI players often have trouble combining their principles the right way, so get them to change civics (you can only ask them to adopt yours, so be careful). Have them adopt civics which benefit them the most and have synergy bonuses. Make them switch from outdated civics. Give them the tech they need to progress. On that topic, you can ask your vassals to research the techs you want them to, so make them research cheaper technologies for you and then accept their trades (they will often ask for twice or thrice the cost, but you have to give them the techs anyway).
Religion is another way to help, have them adopt the right religion (yours if possible) and make sure all their cities have it. +5 from religious unity may make the difference.
On the foreign front, bad relations make things worse, so try and avoid it if possible. Once again, religion helps. If all your vassals have the same, the will have good relations among themselves (and with you).
The expansion shouldn't be a problem. The military front is rarely a problem, safe if Siberian or central asian barbarians are wiping the floor with them (happens when they fall behind techwise). In that case, help them.
The main problem is the economy. Unless your block researchs fast enough, their economy is unlikely to grow fast enough to avoid becoming an unstability factor. The way to compensate this would be to help them grow fast enough and (cause it's really hard to avoid the recession unstability for a vassal) to have positive stability from other factor to cushion it.
Going from stable to colapsing so fast sounds like a bad civic combination + loss of resources becoming a source of unhappiness, tho there may be another reason. Gifting they cities is only a temporary solution thanks to the extra expansion stability