As someone who has gone through this very exercise just recently, I can safely recommend the Canon 35mm f2.0
Firstly, you definitely don't want to blind the baby, and even bounce flash causes his/her eyes to close tightly.
You also definitely want a fast lens - and here I wouldn't recommend anything slower than f2.0.
I first bought the highly rated Canon 50mm f1.4, but found it WAY too zoomed in on a 1.6x crop factor. I also found it to be very soft wide open, meaning it needed to be stopped down to f2.0 or f2.8 before being sharp enough anyway.
After much research I settled on the Canon 35mm f2.0. It is very sharp at f2.0 and has obviously a much better crop factor. It's very reasonably priced if you don't want to buy L glass.
Another lens which appears to be a very good option is the Canon 28mm f1.8. It costs around $460. I have not personally used it, but I am interested in getting it.
PS: Don't forget to set your white balance else your pics will be way too warm.