MSNBC has a story about the Coqui (Eleutherodactylus coqui) situation in Hawaii. These tiny frogs are native to Puerto Rico, and were accidentally (and probably intentionally) introduced into Hawaii during the 1990s. Hawaii has no native reptiles or amphibians, and the Coqui has quickly become a major competitor for insectivorous birds.
The eradication techniques listed in the article are pretty interesting. One involves spraying the frogs with a massive blast of caffeine, causing them to die a horrible, twitchy death. Another involves applying lime to dry the frogs out. Officials admit that they wish they had dealt with the Coqui when the frogs were first spotted in Hawaii, but even now delays in permits and funding continue.