How can I find a new charger for my Rio Riot?

SOURCE: Rio Riot

Have a try with this one:

http://www.digitalnetworksna.com/support/rio/downloads/rmm/Rio_Software_Ver260.exe

Although not officially available (or supported by DNNA) for the Riot, it happens to function with the Riot as well as newer players. Potentially later updates to RMM might break support with the older players.

SOURCE: What size plug fits into a Rio Riot ipod so that I

You should be able to use the sync cable you charge it with along with a cigarette adapter that has usb ports on it. I hope that helps.