Try this Weldbond glue. It dries clear and doesn't take to long to dry. It stick to painted surfaces as well as cloth. I glued some felt on the bottom "base" of some crosses I made and it sticks good. I messed up on putting the felt on one of them and it was a chore to get off. I think you will really like it for what we do. I wouldn't use it to glue cabinets or furniture up. I would use Tite Bond II or some thing like that.
http://www.ebay.com/itm/5-4-oz-Weld-Bond-Glue-by-Weldbond-8-50160-/370798072574?hash=item56554992fe:g:gAUAAOSw7aBVJsW6