Shame that neither resources nor an active modding community are available to answer these kind of basic questions.
I think I've figured this out via trial-and-error:
Custom supply ship blueprints must use the RequiredSpecificComponents tag for SupplyModule.
Using the RequiredComponentType tag for SupplyModule will not work - the blueprint will be accepted by the game but will not appear in the in-game build list.
Further, the RequiredSpecificComponents tag requires the presence of a RequiredComponentType tag in the blueprint or else the game will return an error on startup.
The modules listed in RequiredComponentType and RequiredSpecificComponents seem to be unrelated - the default blueprint for supply ships uses LifeSupport for RequiredComponentType and SupplyModule for RequiredSpecificComponents.
To be honest, the way it works seems rather stupid. But if you create your blueprint using the above guidelines, you'll be able to get your custom supply ship into the game.