A lot of it is still dependent on the circuitry. Is the circuit multiplexed? What do the digit drivers look like now? How many displays are there?
The general way to do it is:
1. put an inverter on every output that leads to the displays, including the common pins. Select an inverter that has the same drive strength as the original circuit.
2. Change all NPN digit driver transistors to PNP, or n-channel to p-channel if using FETs, and vice versa.
Change their common pin (usually GND for common emitter config or VDD for emitter follower) to the other supply.
That's the basic steps. It could be easier if more of the circuit was provided, I don't know what's in the circuit right now to make a really good judgement.
(EDIT: Since now it's know it's charlieplexed, this special mutation of multiplexing will require unavailable driver inverters. You may try to build custom tristate inverters that will somehow tristate automatically when a tristated input is detected. This can get very complicated and the previous suggestion to get CC displays stands.)