Many different types of adhesives can be very useful in this situation. Something that I've seen used a lot is adhesive putty also known as sticky tack. Adhesive putty is a bunch of small strips of a sticky substance a bit like dough that is commonly used to hold things up. You'll want to roll them up in little balls, then stick them on the corners of the photo frame, then put it on the walls. You may need to add the putty in more places if the picture is too heavy.
In this answer I describe various alternatives for how to hang something on a wall.
In your case you might need something tolerating a heavier load, and my suggestion to you is that if you have wooden lists in the roof you could possible attach nails either to the list itself or wedged in between the list and the wall or roof. Then you attach strings to the nails and hang your picture from these. This method will leave virtually no marks and should be allowed by your current lease options.