Yes, it stinks that some of UA's planes do not have changing tables. That's true for some of DL's planes, too. (I don't fly AA enough to know for sure.) Yes, it's tough to change a 19-mo old on a toilet seat, but I assure you I've done it many, many times. A changing pad and sanitary wipes are your friend. It's all part of traveling with a youngster.

I agree with the previous posters that it is quite presumptuous of you to want to change your child on what in all likelihood was the FAs' seat. Moreover, I'm appalled by those that think it's OK to change diapers at the seat (I realize the OP was not advocating that), and would invite them to spend the entirety of their next flight sitting in a well-used lav if they don't see the issue.