I decided to do a visual survey, so I searched 'autoharp music' on YouTube. There are many, many videos there.

It is clear that one can play autoharp by holding it against your chest or by putting it on a table (or floor, if you're limber). If I were using a table, I would try putting the instrument at various angles in order to see which worked best. I might want to secure it down with plasti-tack or shelf liner.