If you plan ahead with a reputable company they can tell you if your child will be allowed. It is not an age factor but size. Sometimes a company might ask for the height and weight of the child just to be sure. Once you are approved it will be time to get the kids excited. Keep in mind that if you are rafting with the little ones you might be going through a smaller, calmer section of the river of course. Sometimes depending on the tour many companies will add an extra guide to be the personal tandem buddy of your small child. This usually has an extra charge of anywhere from $20-$30.
Doing adventures with young children is where it becomes beneficial to contract a local outfitter or tour company for an entire week package. They will do all the leg work of where you can and cannot venture with the kids. Companies like ours, we own our rafts, have our own zipline and tarzan swing, and bring our boards to the beach so we can pretty much make it happen on a personalized private adventure.
If your kids are adventurous Costa Rica is the perfect option for letting them feel like they are putting on their big boy/girl pants!