Keep an eye on the background.
Since the baby will be in his cradle or cot and as you look through the viewfinder, it will be too easy to concentrate only on the subject, and assume that all will be OK. If you overlook clutter which will distract the eye in the final print, the result might just be messy.
The odd detail to give context to the shot is fine; a soft toy, a set of pram beads all help. But as you size up the shot, be careful to discipline your eye to see the whole picture, not just the sweet little face.
Lighting will probably be poor. Luckily, it will also be indirect; the sides of a pram or baby's cot see to that, so the effect will be appropriately soft. However, you might consider using some sort of support for your camera - so go prepared.
Some of your shots will include the parents. Again, remember the whole picture. Frame the parent/child shots against an unfussy background; it's surprising how often doorframes, light fittings etc. spoil the composition in informal indoor shots.
If you take (are allowed to take!) shots of the child being breastfed, or for that matter being cuddled in a similar position, then it can help if the mother loosely wraps a shawl around the baby and her supporting arm. This reinforces the line of the arm and so emphasises the cradling action and the maternal comfort and protection. It also covers up, or at least draws attention away from, any crumpled baby clothes, leaving the face the centre of attention. If you move slightly to one side so that the mother's face, slightly out of focus, can be seen at one edge of the frame looking down at her child it can add something to a mother-and-child image.
Also, take lots of pictures and weed out the rubbish before you show the results! I've often done this job for family and friends, and know the value of overkill.
Good luck!
