A lot of airlines actually don't have changing tables on their smaller aircraft. The problem with United is that they do have some pretty longish flights on those 757's.

You kind of think they can put at least one plank of wood in one lav somewhere on each aircraft....

First, change your baby in the boarding area, even if not absolutely necessary. Then use those "Nighttime" diapers like the pp mentioned. If your child is in between sizes, go for the larger one but make sure to use some of them before leaving to be sure they fit (i.e. no leg gaps).

Also practice changing your child standing up before leaving, as soon as the child can stand with support (i.e. pulling up). This is a helpful tip anytime in public when you don't have access to a changing table.

It's not recommended to change your child in the seat. Parents do anyway, despite the complaints. If you want to "risk" the wrath of those around you, just don't hand the dirty diaper to a Flight Attendant!!! (They're not supposed to handle them anyway and the waste containers are treated separately coming from the galley vs. lavs).

Keep your child in changing-friendly clothes. If you must dress him or her up to see the grandparents, change the clothes after landing!

I'm not sure of this and too lazy to look on Seatguru but often the handicapped lavs are a little bigger. I've noticed that on the newer planes, this is not always the case but it's worth checking out. A bit more space might make the task easier.