Some glues and also most oil paints melt polystyrene, so specify.

Kat's idea of wood strips (fence palings?) is good, but I'd predrill for the nails, unless you have a nailgun. Or use screws. It will never come unstuck again, particularly if you clad the house all the way round. Was it?

It is common here to glue and staple polystyrene foam on and the spray with a cement texture finish. The staples are just to hold it until the glue hardens.