Currently it is not possible to access the inventories of minecarts, one possible way this could be implemented is to have a detector rail next to the computer and if a minecart that contains a inventory is over the rail then you can access the inventory for it as you would with other inventories.

another Method could be a block that redirekts all getCapabiltiy calls to the entity standing at a specific side. THis way alot of other stuff could be supported.

I think this is a neat idea for a peripheral mod, but not something I want to add to CC. It should be possible to turtle.drop/turtle.suck into a minecart, but that's as far as I want to go.