Thanks, both of you, for the suggestions. It does seem as if the double hibiscus types bloom particularly well. And I can especially recommend variegated abutilons, as they look flashy even when not in flower.
I also received e-mails that mentioned a few other plants. Phonemom seconded my suggestion of geraniums (pelargoniums), and also mentioned orchid cacti and African violets. Christmas cacti can be counted on to bloom in the off-season too--and not only at the holidays. Many of the new yellow types will flower in fall instead. Martynt recommended euphorbia lophogona, which sounds like a good one.
Thanks again, everybody, for your input. I probably should have included phalaenopsis orchids as well, since they are among the easiest orchids to purchase and care for, and their blooms last a long time. Please keep the suggestions coming!
Someone also asked me whether allamanda was related to mandevilla. From what I've read, I think they are close kin. If anybody knows for sure about that, feel free to let us know. My allamanda is one of the "bush" types, but there are "vine" types as well.