from what your saying its that the tree is causing the damage from what ? is it branches falling of the tree on top [roof] of the greenhouse and does this happen when its windy bringing down the branches
if the pieces falling of the tree are small but are breaking the glass then as Andy is saying strong perspex
or plastic sheets cut to size could be an idea fixing with W clips now and if your greenhouse has a gulley where you fix the glass into you could consider getting some strong weldmesh or reinforcing steel mesh that's used for reinforcing concrete placing it on top of the greenhouse and securing it so it fits over the top
so the pieces fall onto the mesh ?
if i had that problem i would be constructing 4 post's at each corner of the greenhouse then put some strong scaffolding netting on the post's pulled tight like a football goal to catch the pieces of wood falling on it although there will be some cost whatever you do its the long term fix?
we had a similar problem [not a greenhouse] but every time you doing something on one part of the plot the tree branches where hitting you in the face so asked the farmer if i could trim the branches and he said not a problem as ling as you don't cut the tree down
so the tree's going to get a good haircut with my chainsaw very shortly as soon as the snow goes and by the time the branches grow back i wont be gardening that plot
hope my comments help and good luck with whatever you decide to do