Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from New York to Branson as you normally would.
For a flight from New York to Branson, you will be flying into Branson. Branson (BKG) is just 7.4 mi from the center of the city. Branson is the only Branson airport and it handles 0 inbound flights from New York per day. 2 airlines have flights to Branson from New York on a regular basis.