The first alternative to TAP would be the 'not TAP', where you simply keep using your current output format. Say you are using JUnit, then you keep using JUnit.
However, if you are looking for another standard for an output format for your tests, then you may have a look at Subunit.
Subunit is a streaming protocol for test results. The protocol is human readable and easily generated and parsed. By design all the components of the protocol conceptually fit into the xUnit TestCase->TestResult interaction.
Subunit also contains a small tool that converts TAP to Subunit.