An easy strategy to defeat Romero, is for a player to lure George Romero to the Mystery Box, and start shooting him. While running around in circles, when your gun runs out of ammunition, keep buying a new gun from the Mystery Box, and attacking him. This is a quick way for players on Solo to achieve this, but it may take a few trires on co-op.
If any player has VR-11 Lazarus and shoots George while he is in the water, he will leave for 2 rounds, but no drops will be rewarded.
A strategy for co-op, is for all four players, wielding strong weaponary, such as the Scavenger, Ray Gun, RPK, HK21. Flopping him with PhD Flopper while doing this will also inflict damage, without wasting ammunition. It might take a bit of time, but is an easy way to achieve this.
The Death Machine is also an extremely effective method of killing him, in both solo and co-op.