In "In the Begining", G'Kar talks about human currency having lost it's value. That suggests that humans have their own currency. I see three possibilities.
1) The "credit" is the human currency. We saw it a lot on the show because B5 was run by EA. Each race has it's own currency we just never heard of them.
2) The human currency, whatever it was, dissapeared after the Minbari war and the humans adopted the "credit" which is an inter-racial currency (like the Euro but on a galactic scale). Some rich races still have their own currency (like the Centauri) but most use only the credit particularly for inter-racial trade.
3) A mix of the two. The "credit" is the human currency but it regained it's value after the war and became the inter-racial currency described in option 2. But that seems kind of a stretch.
I think option two makes a lot of sense. The Narn economy, was destroyed at least twice so it would make sense that they don't have their own currency. Minbari don't seem to do much trade internally so just using galactic currency would suit them fine. And the League, being a group of small nations would use it for the same reasons Erope uses the Euro.