Build a PVC frame with attached black curtains that you can put the items behind. If you do it like the folding stage, the curtains are attached (no taking them off and on).

We use different backdrops in our Children's Ministry skits. We have several tripod uprights (find them at a camera store/supply, used for hold up backdrops). We drilled a hole in each end of a PVC pipe and put it between the tripods (there is a small upright piece on the top of tripods that the hole in PVC slips over). If you made a black curtain, you could slide it on the PVC (paint the PVC black). 

We have prop holders (prop rails) like Shawn suggested. But sometimes our space is very limited, so we put the props, etc., in boxes (per song) and bring them out one at a time. We have also made a frame from PVC that sits on the floor, put upright pieces on it and stuck our prop handles in those.
We do either (a) use black foam core or sintra so our props are black on the back, or (b) glue black felt or posterboard to the back.

We put very small numbers (color coded) on the back of the props, so we know which song and which puppeteer the props belong to.

http://www.childrensministry.org/howto/howto5.htm

See if that helps.

We are traveling on Jan 27th and I am making the "flats" out of PVC.  I like several of the ideas but I think this is the one I'm going to try first.  I will do my best to get a picture!!! I'm always so busy I forget pictures.

Indexing props, great idea, so organized. Good luck angel hope it works out good.

We practiced yesterday and just decided to use the 4x8 foam insulation boards we have that are painted black.  I may still make the pvc flats but time is of the essence right now and these will do the trick. I hope!!