Ask Mr. Smarty Plants

We always like to start out knowing what kind of plant we are talking about. In our Native Plant Database there are 18 species of the genus sedum but only one of them, Sedum ternatum (Wild stonecrop) is native to Ohio. This really doesn't matter, as we already knew that 'Autumn Joy' is a selection of some native sedum, or possibly a hybrid of Sedum telephium. They are all members of the Crassulaceae (Stonecrop) family, and have pretty similar growing conditions and pest problems. We had a little trouble finding any information admitting that sedums HAD problems with insects, but these two articles give us some clues.

From Washington State University Extension for Whatcom County Stonecrop - says few pests bother with sedums, although slugs will sometimes take a bite. That is not surprising in view of the fact that the sedum characteristically grows near the ground, where the slugs are grocery shopping.

eHow Home Sedum Plant Pests - concedes that there are several bugs that will damage sedum, but the two it mentions that are good possibilities are aphids (they attack everything), and fungus gnats. Because you specifically mentioned tiny black bugs, we're thinking that might win the prize. The fungus gnats actually originate in damp soil around the plant, and this article mentions a couple of ways to deal with it.

Since the fungus gnat became our likeliest suspect, we found another article All About Fungus Gnats which suggests, among other things, letting the soil dry out before you water it again.