Place the melon in the bottom of the cooler. Using a sharp knife, or apple-coring tool, carve a 1 1/2-inch hole in the top of the melon through the center of the melon. Open the vodka and place the neck of the bottle in the hole. Use rolled towels to keep the bottle upright in the melon.
Fill the cooler with ice and cover the ice with aluminum foil and newspapers to keep the cold inches (This is assuming the cooler will not close because of the bottle).
Leave overnight for vodka to be absorbed into the melon.
Remove bottle and cut melon in half, then cut flesh into chunks (or use melon baller if desired). Mix in large bowl with sliced lemons and cilantro if desired.
Note: Leftover "water" in the serving bowl makes a refreshing cocktail; serve over ice.