2010-11: Danny Moynihan played for the New Hampshire Junior Monarchs U16 team. He scored 14 goals with 6 assists and 30 penalty minute in 37 regular season games and scored 2 goals with 1 assist in five playoff games.
2011-12: Moynihan played junior hockey as a 15-year-old — skating in two EJHL games and 21 games for the New Hampshire Junior Monarchs in the Empire Hockey League — and played with the club's U16 team. He scored a goal in his brief EJHL stint and scored 11 goals with 8 assists and 16 penalty minutes in junior B play.
2012-13: Moynihan played for the re-christened Middlesex Islanders' U18 team in his third season with the organization formerly known as the Monarchs. In 32 games he scored 25 goals with 15 assists.
2013-14: Originally intent on playing college hockey, Moynihan and younger brother Connor Moynihan joined the defending Memorial Cup champion Halifax Mooseheads in the QMJHL. The only player to skate in all 68 games for Halifax, he scored 9 goals with 17 assists and was +8 with 66 penalty minutes. The Mooseheads finished first in the Maritimes Division and reached the playoff semifinals; falling to Val-d'or In a seven game series. Moynihan scored 3 goals with 4 assists and was +6 with 6 penalty minutes in 16 playoff games. He was ranked 77th amongst North American skaters in Central Scouting's final rankings prior to the 2014 NHL Draft.