Not as familier with coastal pythons as I am with ball pythons but getting non feeders to eat methods are pretty much the same for all species.
First, are you feeding mice pinkies or rat pinkies? Coastal babies should be able to handle rat pinkies fine. Note that I am not completely sure if coastals can eat rat pinks out of the egg or at 4 months as I am not sure if the baby coastals I have seen myself were the same age. If you have been offering just mice pinkies, try a rat pinky or mouse fuzzy. A small size prey item may seen not worth the effort for the python.
You can also try braining the pinky or fuzzy (slitting open the brain case (top of skull) to explose the brain often triggers eating).
Placing the pinky or fuzzy (either frozen thawed or live) into a bag then put in the snake, (a pillow case can be used as well) then placing this into the cage over night can get the snake to eat.
Other things to check is the cage setup. Does the snake have enough hides, space, and the right heat, humidity?
Is the snake captive hatched or wild caught? Wild caught are more difficult to acclimate than captive born. Also, check it see if there is any sign of external parasites. Small black specks floating in the water dish after soaking will indicate mites.
Contact the breeder you bought the snake from and ask what prey items they were using and what color. (yes color can play a factor, even pinkies can show dark colors. SOme snakes won't eat white mice/rats, but eat darker ones fine and others are the opposite). Also, by contacting your breeder you can find out how often the snake has ate before you bought it, what size t hey were feeding, if it was alive, fresh killed or frozen thawed, also what type. Some may be feeding hamster or gerbil pinks instead of mice or rat pinks.
Another thing that can be offered is adult mice/rat tails or partial tails. Some snakes will eat this instead of the whole animal and it's one way to get some food into them.
As a last resort force feeding can be attempted. But keep in mind this is very stressful on the snake and could just make the problem worse. If you have never force fed a snake before then take it to a qualified reptile/snake vet. They can inject nutrients with a needle or via a tube down the throat (ie tube feeding) if the snake's condition is deteriating.