Use a CA glue with activator, medium is PLENTY strong
I am often afraid of CA glue because of the very short set time. These really don't leave much margin for error. I'm not sure what I would do with the activator in this case since I have small objects of irregular shape and a surface that is already finished so has to remain clean other than the spots where the objects are attached. I suppose I could spray the activator on the back of the objects and put the glue on the painted surface, but again, there is no margin of error here and no chance to make adjustments and clean up excess glue. If I use a super glue, it would probably be a single component with a >30 second set time. That would be long enough to position the object, adjust it if necessary, and wipe up excess before it sets.
On woodworking for mere morals he talks about a glue I think its call weld bond. This glue is suppose to glue painted surfaces together without clamping them.
I think I can get this at Michael's, so I will check that out. I might also mention that I am short on time, so I really can't order anything. That would leave me something I could get at Home Depot, Lowes, Walmart, Ace, Michael's, etc.
Are you sure you want "glue'...and not just a few dots of Caulking/Silicone to hold them in pace? Even "regular" latex caulk is a pretty good bonding material.
Something like that might work. There are two issues here. I have several small wooden stars to attach, some of which are a bit warped. They are about 3/16" in thickness, so they are flexible. There are allot of things that will secure these, but I am worried about the warped sections pulling up the paint that the glue is secured to, especially since the paint is just a few days old an not cured. Because of the flexibility of the caluk, I would expect it to have difficulty holding down the warped edges. I have looked at construction adhesive like liquid nails and the Gorilla brand.
I am considering tracing out the stars with a fine pencil and using a dremel with a sanding disk to take the paint back down to wood where the stars will attach. Since the stars are wood and the backs are unpainted, I could use a good wood glue to attach them and have no fear of them pulling up at the warped edges. The rest of the figures are 3/16" cardboard that has been painted and finished with 6 coats of gloss acrylic. These would probably stick on with a bit of chewing gum and stay just fine. For the cardboard figures, I am only worried about the glue solvent delaminating the enamel paint on the surface or damaging the cardboard.