Most newer planes have at least one changing table on board, but they are always small: a toddler isn't normally going to fit on it. The normal design is a fold-down shelf over the toilet in the WC. On most planes, the best spot is the floor just *outside* the WC, where water is handy to wash your hands when you finish, and the diaper may be disposed of in the trash. Bring your own changing pad, the larger the better. (A good choice for air travel is a "chuck", the disposable absorbent squares used in hospitals and nursing homes. These are also good for putting in hotel beds when kids are prone to night accidents.) Obviously, carry lots of wipes and ziplocs to dispose of messy stuff and/or seal up dirties to be washed later.
If the seatbelt light is on, you will have to change the diaper at your seat, perhaps in your lap if every seat is taken (again, a chuck can come in handy!) Make sure you have everything as easily to hand as possible, NOT in the overhead bin, b/c you can't get to it if the light is on. People around you don't want to smell you change that diaper, but that's better than letting the odor waft b/c you are stalling on changing it. Be as fast as you can, and get the diaper sealed into a bag to kill the smell ASAP. Airsick bags are good for diaper disposal.
FA's handle food, so they are not allowed to touch any item that has come into contact w/ human waste of any kind. They cannot touch the diaper or the small bag that it is in, but they can hold out a trash bag and let you drop it in.
One other thing: if your older baby is in a carseat for a flight longer than one hour, I suggest using an overnight diaper for the flight. The position that a child is in when in a carseat will put pressure on the tush in such a way as to make leaks more likely with a regular diaper.