I wouldn't use felt, because I don't think you could wash it.
I have seen some curtain rods that will swing out of the way, like a door. Actually, like the old towel racks people used to hang in the kitchen (only they had three arms) I don't know how long of an arm they have, though.
It doesn't looke like you have enough room for one on each side. You need someone to engineer something for you that would fold up accordion-style, and still support the weight.
Good luck with this!