the "cup feeding method", I think, refers to a practice of putting the snake with the food item in a very small container, such as a deli cup transport container, and to leave them like that over night - in a temperature appropriate location of course
I have gotten snakes to eat that way a few times, so it's definitely something to try
I myself don't feed live rodents, but for those who do: this should never be done with live rodent prey