It is highly unlikely, if the screen is manual, that it weighs more than about 30 pounds or so and standard drywall anchors should be more than sufficient.
If you go to Home Depot or some other hardware store you will find a product called EZ Toggle which are similar to toggle bolts but offer greater weight capcity, without a hole that a bolt can fall through. You just drill a hole (they'll tell you what size) and then slide the EZ Toggle in then you have a secure hole that the bolt can go into as deep as you need it to. Then just hang the screen on it.
If you look at the image below, this was my old 106" diagonal manual screen and it is on L brackets that are just using standard drywall anchors. No issues at all with the screen... though it was replaced with an in-ceiling electric model.
If you are
super paranoid of the weight, then you can always get a 1"x1/2" piece of wood from the hardware store, cut it to screen length, screw it into the studs on the wall, and then hang the screen from that. It will ensure proper support.