Converting a Coleman lantern from oil or gas to an electric lantern takes special skill. While the benefits may vary, you do reduce the risk of a liquid fire greatly. It is important that you hire a qualified electrician to complete the task. You do not want to risk the chance of a short or electrical fire. You can also ask the electrician to fix the lantern so that of you ever want to re-convert the lantern back to oil or gas, it can be done so in easy steps.
Purchase a lantern conversion kit from your local sporting goods store for an oil or gas lamp burner. Most conversions kits are sold in various sizes and can be bought in lamp repair and supply shops. Make sure you buy the same size kit as the burner on your lantern.
Take your original lantern to a qualified electrician to have it converted to electric. You can purchase a replacement burner for your lamp and have the replacement converted if it makes it easier. You have to buy the same size unit as the one you are replacing, or it will not work.
Unscrew the original lantern burner from the inside and place it in an area where you will not lose it. Should you decide to convert the lantern back, you will have an undamaged original part to convert back with.
Screw into place the electrified lantern burner from where you took the original off. Use a knife to cut out the portion of the lantern where the wick is in place. Make a hole roughly the size of your light socket -- e.g., 1 to 2 inches around -- in the bottom.
Drill a hole in the lantern that is large enough to pass the electrical cord. Insert the light socket and wire it through the holes. Place one end of the wire and install it to the socket while attaching the plug into the other end to form the cord and complete the circuit.