My games tend to end by diplo or culture long before the space race begins, so I actually want to play a space race game. I know Babylon and Korea have science bonuses, but who else would be a good science civ?
Many are suitable, but they all use slightly different tactics added to the same strategic core.
With Poland for example you get free SP/tenets and with that you can get pretty fast through Rationalism and to Scholasticism, which can really boost your tech lead. There's a strategy with a mixed Tradition/Liberty opening with that Civ (Poland's UA lets you do it without delaying the opening of Rationalism) described in a thread on the strategy & tips MB that really puts you in a good position for a SV.
The rest is the usual: heavy growth, good focus on getting the Science techs and putting up the science buildings, focus on farming/getting GS for Academies (ideally 3 or 4 around your NC city) and, if required, GE in good time to get the key science Wonders. GS for Academies until Public Schools, then saving them for bulbing in the late game, starting 8 turns after your Research Labs are up, though waiting even more can be beneficial too (if there are still ways coming to increase your science output, eg: Worker's faculties, several CS still left to ally, some big cities you might be able to obtain etc.). Having good Faith production for the endgame is a big plus, since it might let you buy more GS at the end. Then there's not missing out on the extra GS from Hubble, from Space Flight Pioneers an eventually from ISS etc.
If you play on the higher levels, then espionage for tech stealing is another key factor, and Trade routes. If there are cultural Civs not far behind you, it can be worth it to make a detour to grab the Great Firewall to negate their eventual Internet.
Not winning diplomatically is a matter of choice. Even with all or nearly all CS as allies, it's usually not enough anymore to win since the Patch. You can avoid Globalization, and if it comes to that, simply not assign all your delegates because, say, in your political vision you don't believe there should be a World Leader and "boycott" the vote.
Not winning by Culture before science is easier on the higher levels where global tech-ing rate is much faster and you miss some Culture Wonders anyway. On the lower ones when you could win almost by accident you need to learn to balance it out more and decided when your tourism/culture are enough. You're not after cultural domination, so you don't need all the Cultural Wonders, you don't need to assign as many cultural specialists, and you can use some Great Writers for culture boosts instead of for Works. You can grab artifacts in your territory or to deny a few to the AI, but you don't go out of your way to get others. You can choose to align yourself ideologically with the stronger cultures, eventually even open your borders for a while (if they're not
too strong) so that you get protected from pressure. If it's not necessary, you can avoid buying OB from the AI over which you'd gain influence too fast, or else compensate for your lower tourism by buying OB and counting on the boost to stray afloat with the tourism leaders. It's quite possible to maintain a fairly strong, reasonable tourism that combined with a strong culture (that you'll want with Poland to obtain SP even faster anyway) that's enough to protect you from an AI winning by culture without risking Cultural Domination before a SV.
With a tall and wide Poland (that's also valid with any Civ played wide-ish, like Germany etc) you can choose Order for the science boost to factories, and make sure your production is up to the task of producing the Spaceship parts, or if you judge your science lead is enough with Space Pioneers + Hubble + Internal Station, prepare to farm or buy a few late game GE and with the level 3 tenet buy a few parts with those.
Having done pretty much all of this in my current Emperor game with Poland, I'm 3 part away from the SV, influential over 5 out of 11 Civs (with no chance to become Influential with 2 of the remaining ones). I have a lead of 12 techs over my next rival and still 3 GS to bulb, and at the bottom of the board Pacal and Morocco get a whooping 18 bpt each from my TR to them.
And you can also go Freedom, and in that case the focus is no longer on your production capacity, but on your treasury to buy spaceship parts (if you play Germany with Freedom, you can do both... extra science with Scholasticism, production from TR to city-states, tenet for influence from TR to CS etc.)
Another Civ I've won some great SV with on Emperor is Venice. It's also fairly easy, but I haven't tried it with anything but Freeedom (I imagine trying to produce or rush with GE the parts when you have only one city able to do it when it's been focused on growth/science to begin with would be a challenge).
With Venice the key is to be super tall and to get very tall puppets too. Getting a mountain for an observatory for that extra 25% is a massive help with Venice (but can be compensated by extra puppets). If it goes too slowly in the late game, buying a few more CS can be important (I bought three on the same turn in the Information era in a SV game, bought their RLs and one observatory and then 8 turns later the strength of my stored GS was much improved). On the higher levels, Venice benefits massively from its double TR in the early game - beakers are flowing in from the other Civs, and this can be prolonged longer by focusing on the top of the tech tree for as long as possible/safe. Piling up the gold to buy the spaceship parts while maintaining the CS allied for science and the rest is easy with Venice.
Those two Civs aren't specifically tailored for a SV (some even find Venice tricky for one, though I don't think so myself), but both these "strong civs" can easily get one. Another with which I found it sort of easy was Germany, with the heavy production.
I haven't tried it with other Civs since the patch, but I imagine the core science/growth strategy is the same. My general idea would to see how you can use the chosen Civ's unique benefits to ameliorate the general strategy for growth/science, and after the Apollo Program, also production or gold.
All civs with advantages for growth should do great, and eventually all those with faith, or gold, or production bonuses should be workable if exploited with a SV in mind.