I have a customer who has a very, very dark room that she wants to take portraits in. I'm photographing a 2 month old baby. What type of lighting should I use?
We take photos with light. You can't take photos in a very dark room.
The usual approach for babies is to bounce the flashes off the ceiling (if its white). This gives a nice soft light.
These photos of my grand-daughter were taken with three small strobes/speedlights bounced off the ceiling.
...first, you didn't say what kind of mood you'd like. Also, you left the question quite general. Hence I'll try to give you some general tips:
flash (like the others said) bounced on the ceiling give a soft look, but usually this scares the babies which are so young, and I presume that the stark contrast of the unexpected powerful light compared with the darkness of the room could scary a lot the baby, hence, because of the possibility of a very unpleasant reaction from child, you will not have the occasion to shot many frames.
there is a logic in light. Why the client wants to shot the baby in there? In what pose? Is better to tell us these things. Perhaps she wants to photograph him asleep? Perhaps the room is important? Perhaps she doesn't want a simple head-and-shoulders portrait but an environmental portrait? Hence I think that's better to have a logic in light. While a ceiling-bounced flash might simulate the normal light which is in a room, perhaps is better to put one or more lamps with lampshades in order to give a different, more intimate mood and make the baby more cooperative. Also, I think that you can achieve a very good mood with this solution.
you can also combine the two solutions above but you must be careful at how the light will fall and also at different temperatures of light (a gel might help). Also in this case the flash, which will act like a fill flash, won't be so scary for the baby.
again, taking in consideration that you need to show also the room, you must have in mind the high ISOs (this applies especially if you use the lamps only), the fast aperture lens (eg. primes) (which gives you low DoF to separate your subject, keep the ISO and shutter at desired values) and in the case of using flash consider dragging the shutter in order to show also what's around.
Good luck and good light!