Looking through the javadocs it doesn't look like you can with just the bukkit API. I could probably write up a quick thing using craftbukkit/NMS code to be able to do it but the problem with that is it will break on pretty much every bukkit update since they implemented dynamically changing package names.
Maybe I could treat it like a normal spawner and use the methods for this in a normal spawner. The only problem I see with this is a casting problem. Spawners are treated as blocks not entities. Maybe I can try setPassenger. Doubt it will work but I can try. EDIT by Moderator: merged posts, please use the edit button instead of double posting.
Yea, that wouldn't work. SpawnerMinecart is an empty interface that inherits from Minecart so there are no methods that would allow you to get the spawner in it or set the spawner in it and if you were to attempt to cast it to a spawner it would throw a ClassCastException. There are still a lot of things like that that aren't fully implemented into the API yet. It wouldn't be too hard to do it through NMS though but, again, there is the dynamic package names problem.