How often do merchants replenish their gold supply?

After two full days of waiting, the Thieves Guild fence Tonilia went from 8 gold to 1000 gold - it's possible that it varies from merchant to merchant, but two days seems standard so far.

42 hours, to be exact. Sell 1000 gold worth of crap at your favorite fence, use the wait option (T on PC, "Back" on Xbox) and wait for 24 hours, then another 18 immediately after. No need to leave the fence's side.

If you are on a PS3/Xbox, then you can either save and kill the merhant and reload the save (this way they are fully restocked), or use the ways mentioned in other answer