Updated June 22, 2014
I found some issues that generated an error, which may not have been seen if your don't play with testingcheats enabled.
I also, tested this with an infant and it is in fact usable by infants too. It's been so many years since I created the first version, it's hard to remember things.
I had a request to have my swing use the textures from the crib.
It works the same as my older version, only the textures are pulled from the cheap crib.
I didn't create images of all of the textures, but any recolors you have of the crib will also work for this swing.
If is found with the child items for $50.
Known issue: If the adult sims removes the child autonomously, the swing does not stop. There is however, an option to stop it manually.