Make the coquito first. Blend evaporated milk, condensed milk, coconut milk in a blender. Add the rum, vanilla, cinnamon, and nutmeg. Blend until all is well combined. Cover and place in refrigerator for at least 2 hours.
While you wait for the coquito to chill, make the donut holes. Heat oil in a skillet until it is very hot (350 degrees F).
Cut biscuits into quarters, and then fry them in small batches for 1-2 minutes or until golden brown. Transfer them to a paper towel-lined plate to drain the excess oil.
Once they are all done, place the cinnamon sugar mixture in a bowl and roll the donut holes. Set aside.
Remove very cold coquito from the fridge. Squeeze coquito into each pipette and place into the donut hole. Repeat for each and serve.