My science captain originally ended up in a Star Cruiser. It was effective enough as a support/healer, though a bit squishier than normal due to the lack of Engineer captain "Oh Sh*t!" abilities. On the plus side, Subnucleonic Beam is a good perk to bring to any PVP battle... down side is maneuvering the Star Cruiser around to actually hit the target that needs to be SNB'd before the opportunity is lost.
I've also briefly tried a Tactical captain in a Star Cruiser. It worked "ok" as a pure beam DPS build that would have done better in an Assault Cruiser or Excelsior. Tactical captain is even squishier than a Science captain, which is saying a lot considering all the self-defense Science loses compared to Engineers when in a Cruiser.
With the sole exception of Excelsiors and Klingon Battlecruisers, I can't help but to recommend Engineers only for Cruisers, it just works the best. Engineers in Science vessels, Science captains in Escorts, etc all have their perks that makes that combo potent... but I've just not seen it with most Cruisers.
The potential damage output of a Star Cruiser is probably the lowest in the game (maybe except shuttles).
You get 2 tac consoles and a tac Lieutenant.Captain abilities of Tacs can't really help here to bump the damage and they do nothing for your survivability. Offensive sci powers usually have a 90 degree arc (bad with cruiser turn rate) and require aux power. There are always ways to work around something, like batteries for the power and Aux2Dampeners for the turn rate, but all these workarounds also require slots of some kind that could be used better. Tac/Star Cruisers are usually a joke and have to be ignored to not waste heals that are better used on other team members.
Sci captains and Star Cruisers are somewhat better, but also not really breathtaking. Dampening field and Photonic Fleet can help with survivability and distract the enemy, SNB and Sensor Scan can debuff the enemy (theoretically). You still will be squisiher than and engineer and can't really compensate with higher damage output. You have to turn your ship to use your SNB and then there is nothing to take advantage of the debuff and kill him before he's able to react.
Support and Tanking is what the Star Cruiser does. Every bit survivability you take away has to be replaced with something else that's worth the loss and the Star Cruiser doesn't have the potential here.
Ergo. If you really have to, use the sci captain. Tacs in Star Cruiser only can deal damage by blowing up next to the enemy, but that's something they do really good.
Every single one of my characters now has a Star Cruiser somewhere in their fleetyards, but not one of them actually use it. I suppose if you PVE a lot, then the Tac/Star Cruiser combination can be very versatile as you can finally manage to have Polarize Hull, Hazard Emitters and Science team on a single Cruiser hull, but if you even look at Ker'rat, you're likely to explode.
Science or Tactical? Science... I suppose.
But even this seems a little unorthodox as the Captain abilities of Science officers don't tend to dovetail very well with the low-ranking positions that ship has in the science department. I'd feel a bit lost as a Science character without my LtCdr and CDR abilities - but this is a personal taste.
The only out-of-class specialization I've found any love for where Science is concerned is in Escorts.