Just use thin nails with picture brackets. You can dab over any holes with drywall patch, which you can buy a tub of at your local hardware store.
You will make holes in the wall if you hang them well enuf so they don't fall. Before you move out you fill the holes and paint the spots. Don't depend on those sticky hooks on painted surfaces. Landlords tend to cut corners and use crappy paint so any tape or sticky hook will probably pull the paint right off the wall.
stand there and hold it up. just kidding, not to worry, patch it up when you leave
If the frame painting is heavy and expensive then glue on hook would be risky, i believe. Why not opt for wallpapers instead.
Get those glue on hooks that release with a pull tab.
Use 3M picture hangers as they do not damage walls.
I'm moving in a rented apartment with very bland walls and I want to put some framed paintings. Is there a way to do it without leaving a trace on the walls?