You can use nontoxic mosquito dunks. These are suitable for fish ponds and horse troughs, so they won’t harm the value of the water.

http://www.cleanairgardening.com/mosquito1.html

Alternatively, you can put a goldfish in the barrel, as long as you are always going to keep enough water in the barrel to sustain the goldfish. This one is a higher maintenance kind of way to handle it, because you have the responsibility of keeping the fish healthy.

If you read the comment on the “Safe Rainwater Harvesting Catchments” page, you’ll see how a reader has described how she uses that method with a fish.