If your child can stand while being changed, you can use the handicapped stall in any restroom (for the extra space for him to stand and you can move around). Some of the handicapped stalls have a sink right in that stall, most at the Studio and AK, since those are newer parks. If he can stand for changing, you could also use the Companion Restrooms.
If he can't stand for changes, your options are more limited.
Some of the Companion Restrooms have permanent counter type changing tables, but not all have them. They are also all counter height (34.5 inches from the ground), so you may not be able to lift a child that size up that high. Most are at least 40 inches long, although some are shorter (one in The Land is only 28 inches long). Some are up to 56 inches long.
Here is a picture of one from Epcot:
This thread has more information about Companion Restrooms, including pictures and measurements of the ones at Epcot - I haven't finished the other parks yet. So much to do, so little time.
As mentioned, First Aid has a Companion Restroom (some are small and none have a changing table). You can also use a room with a cot in First Aid for changing. Some of them are in actual rooms, with a door that can be shut and some have a curtain. All would provide a degree of privacy.
The height of the cots vary and there are some rooms which have an adjustable height cot.
Here's a picture of one of the First Aid rooms:
