The Matchmaker comes at the same dates and times regardless of what character you have.
Depending on what time of the day your Tamagotchi was born, the Matchmaker will start to come at age 6 or 7 (if you started your Tamagotchi early in the day, the Matchmaker will most likely come at age 6. If you started your Tamagotchi later in the day, she will start to come at age 7).
Times the Matchmaker comes: 10:30 a.m, 3:00 p.m, and 7:00 p.m.