Since you are renting the carts, I would recomend just strings of 12v lights with a 12v DC accessory plug and a jump box (like those used to jump start cars) that has the accessory outlet. It can be secured between the front and back seat and recharged as needed.
But if I where to do it on my own carts I would have one of two options for a temporary setup.
Option 1 - buy 12v based lights, create a custom harness with alligator clips to clip onto the battery terminal. The electric golf carts are mostly 36v or 48v, there are some higher voltage but not many. With a 36v cart the configuration is 6 6v deep cycle batteries in series, the 48v is 6 8v batteries in series. Both styles of carts operate their 12v systems off just 2 of the 6 batteries, this too can be used to power the lights. If you clamp the negative of your lights to a negative post of one battery and the postive to the positive one battery above in the series you will get 12-14v (depending on the cart type) and the lights will work. Now, I recommend even with LED, put a switch on them so you dont draw down those 2 batteries all the time, over a long period its not good for the battery and can affect the overall carts performance. If its a gas cart, then there is only 1 12v battery and its just like any other car.
Option 2 - Using standard 120v strings from home. This too can be done, but you will need an inverter. You can get one for about 30-40 bucks that will come with alligator clamps and produce enough wattage to run the lights. Again, you need to hook up to 2 of the 6 battiers in series by using the positive of one battery, and the negative of the next battery down the series. This will produce the acceptable 12-14v the inverter needs to produce the 120v to run the lights.
If you chose to use the carts battery system like above, just be careful to hook it up properly to avoid damaging the carts electrical system. And do not make any permanent modifications to the carts headlight or tailight systems. Even on my own carts if I where to add a permanent way to connect the lights, it would be on its own switched and fused circuit.