Most of my dcks have been enrolled older than baby stage. But the 1 I currently have started at 3 mo and I had to sleep train her. They used a rock'n'play, swing, car seat, all tucked up snug and cozy with a blanket at home or held her til she fell asleep.
I've got another one coming early fall and mom says he falls asleep in the swing, rock'n'play, arms, etc. So another one that will have to be trained.
I simply tell the parents I'm not able to do all that and have a print-out posted on my bulletin board informing them about safe sleep.