I'm surprised we can't do this.(Especially after the feature to counterfeit casino chips was introduced in Fallout New Vegas' Dead Money addon)
I doubt that they have very good ways of verifying the authenticity of gold coins in Tamriel, so there should have been an option for a player with a high smithing skill, or maybe an extra piece of equipment like a mold(one that could be stolen in an unrelated quest), to be able to make counterfeit Septims from Gold Ingots at the forge.
Maybe.. 1 Ingot = 50 Gold
Seems reasonable, since raw gold is hard to come by and unless you're properly equipped, transmuting iron ore is very time consuming.