Assuming you can maintain a stable environment in such a small body of water, your primary challenges will be anemone size, and anemone movement. All clown anemones can easily outgrow a 10gallon tank. Additionally, you will need water movement, and anemones can easily move around a small tank and get sucked into water intakes, powerheads, etc.
If you can find them, the two smallest clown anemones are H. malu and H. aurora. Both species are sand anemones, so they tend to want to stay low in the substrate, and their light requirements are moderate. If you can find a really small BTA, and keep it under bright light with minimal feeding, it will tend to stay small with shorter tentacles... but not always
If you aren't set on having clowns and anemones together, or don't really care whether you have a clown anemone, there are other anemones (and anemone-like creatures) that would be better suited to small tanks. Mini-maxi and maxi-mini carpets, zooanthids and palys, and ricordea would work well. There are also some LPS corals with anemone-like polyps that might work.
