Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Newark Airport to Morgantown as you normally would.
For a flight from Newark to Morgantown, you will be flying into Morgantown. Morgantown (MGW) is just 2.3 mi from the center of the city. Morgantown is the only Morgantown airport and it handles 0 inbound flights from Newark per day. 0 airlines have flights to Morgantown from Newark on a regular basis.