Books and songs
From the time they were able to hold something, I would always give them a little book to hold and look at while we changed (also occupies their hands). My husband and I would also sing a silly song for nappy changing that I made up. They rarely wriggled, but I don't know if it was the entertaining ritual, or not.
You are welcome to use my song for non-profit purposes.
"The Nappy Time Song"
Oh, it's nappy time
Oh, it's nappy time
Nap, nap, nap, nap nap nappy time.
Oh you're a baby, a baby girl*
And you have a chou-chou, chou-chou chou pet-pet#
[You can repeat while taking off dirty nappy and cleaning bottom]
********
Oh, it's nappy time
Oh, it's nappy time
Nap, nap, nap, nap nap nappy time.
Oh you're a baby, a baby girl*
And you have a clean pet-pet
Oh it was nappy time
And now it's snappy time
Nap, nap, nap, nap nap nappy time.
[Sing this verse while putting on clean nappy and snapping up onesie, etc.]
* Or "baby boy" depending on your child's gender
# "Chou-chou" means stinky, pet-pet means bottom or bum