Things You'll Need
Mineral spirits or paint thinner
Oil-based (alkyd) paint primer
Acrylic latex paint
Unfortunately, none of these ideas are guaranteed to work; some unpaintable caulk is truly unpaintable. If that's the case in your situation, your only choice will be to remove the old silicon caulking. Refer to my related article: "How to Remove Silicon Caulking" (see Resources below). Before you buy any caulking it's a good idea to explain your application to the folks at your home or hardware store and get their recommendations on the proper caulk to use. New products are constantly being developed, and one of the really good new ones is "paintable silicone" caulking, a product that combines the durability and long life of silicon caulking with the ease of cleanup and "paintability" that are characteristics of latex caulking.
There aren't any solvents or chemicals that make removal of silicon caulking an easy job. Perhaps the best way to remove it is to use a sharp utility knife or razor blade to cut out the majority, and then use a razor blade to scrape off the residue. Remove silicon caulking with care; your knife could easily slip and give you a nasty gash.
How to Paint Unpaintable Caulk. There are two kinds of caulking in this world: caulking you can paint and caulk you can't. Basically, latex-based caulks are paintable while silicon-based caulks are considered unpaintable. However, everybody makes mistakes and one of the easiest to make is using the wrong kind of caulking. If you ever make the mistake of using silicon caulking in an application you want to paint (around a window for example) or you've moved into a home where a previous owner used upaintable caulking, before you start digging out that unpaintable silicon caulk, you might try one of these ideas. You may just save yourself a lot of work.
Rub a cloth dampened with mineral spirits or paint thinner over the silicon caulking. Allow it to dry and then apply two thin coats of an oil-based (alkyd) primer. Be sure to allow the first coat of primer to dry before applying the second.
Once the primer has dried, apply your chosen paint color, again allowing the first coat to dry before applying the second.
Alternatively, use rubbing alcohol on the silicon caulk and after it has dried apply two coats of shellac. Once the shellac has dried you can apply your chosen paint color.
Use latex caulking right on top of the silicon. Apply a bead of the latex caulking, then use your fingers dipped in liquid dish soap to spread it thinly over the surface of the silicon caulking.
Once the latex caulking has dried, you are now ready to paint it the color of your choice.