OAuth 2.0 authorization servers provide support for four main grant types according to the OAuth 2.0 specification. They also allow you to add custom grant types and extend the existing ones.
See Writing a Custom OAuth 2.0 Grant Type in the WSO2 identity Server documentation to implement custom grant types for the API Manager.
Are you using WSO2 Identity Server 5.1.0 as the Key Manager? If so, be sure to install WSO2 Identity Server 5.1.0.