Keeping pets out of baby’s room

I’m looking for ideas on what to use to keep my kitties from going into the babys room, I just don’t want them climbing all over everything just yet. Anyways I’m trying to avoid putting an air conditioner in his room and if I leave the door open plenty of air would go in from our main AC but I haven’t figured out a way to keep the cats from going in there. I was thinking a screen but I feel like they would still be able to jump through it. Any suggestions?