Borrow a baby and use a small tape recorder! Then you can hide the tape recorder in the crip so it can't be seen, any time an actor reaches in, they can hit the Play button. If it needs to cry when no one is near, run a wire to a small speaker in the crib, the stage manager can hit play from backstage.

If you can find someone on campus that owns a digital sampler,
(electronic music keyboard)they might be willing to help you. They would
have to be reasonably skilled with the instrument but if someone such as
that were willing to help,you could have a set of bawling and cooing babies
literally at your fingertips for split second cueing. Simply press whatever
key you have assigned each baby sound and if it is properly edited, the
desired effect will be instantanious. Your sound techs will have to stash as
good a speaker as they can find in the crib as mentioned above. The CD is
the next best notion with control and multiple FX being the only real
difference. Some of our shows have enough babies in the house that no
one would notice the one on stage. We present to tourists half of our
season so kids of all ages come to the annual melodrama.