If your child doesn't like getting his photo taken (which a lot of kids don't) then I can strongly recommend giving them a cheap and cheerful camera as a way of getting them involved in the process - and even start to enjoy it.
There are loads of different types on the market depending on the age of your child, but for toddlers and preschoolers I would definitely try to get one like the KidiZoom that is pretty much child-proof, as they can and will drop it! It really does need to be able to withstand some knocks. For older children you can get one that more resembles an adult camera. Some other things to consider would be:
Ease of Use Also make sure that it is easy enough for your child to use on his or her own without needing your help all the time, as they will quickly tire of something they can't operate themselves.
Memory size. Make sure it is reasonably big, or, better yet, has the facility to add in a memory card, as they will take a lot of photos and you don't want to be downloading photos every day, especially if you are on holiday. (Callum does like to see the photos he's taken but as his camera also has the facility to view these through the TV, so I tend to do that if I can get away with it)
Megapixels If you want to be able to print any of the pictures your child takes, then look one for that has pretty decent resolution - many cameras are designed to be used more like a toy and will produce images that are fine to be viewed on screen or shared by email, but will only be able to be printed at quite small sizes.
Zoom & Flash You want your child to be able to take pictures in pretty much most situations so I would make sure that it also has some basic features such as a flash, zoom and playback.
The model you choose will all depend on the age of your child, and just how much you think they are going to like photography - some older children will need a good point and shoot, whereas younger children will only need one that is more like a toy. Here's a link to an article which gives you some features to look for depending on the age group of your child which gives much more detailed information than I have here.
If any other moms have already got their child a camera, please leave a comment to help others know what you thought!
Other posts you might like:
Best Mom Photography Blogs
Mommy Stop Taking My Photo: Part 2