I can't help with a list of ships participating in Operation Magic Carpet, but my father was on one ship that participated. He was assigned to the USS Pickens(APA190) when the war ended. He participated in three crosssings bringing back troops. During the first trip, they picked up a few soldiers from Japan, then went down to the Philippines to pick up more troops. The Pickens went back at least two more times to pick up soldiers from the Philippines and delivered them to the west coast.

So, if your soldier or sailor was in the Philippines at the end of the war, there is a chance they came home on the USS Pickens.