This info is for the v4 not sure if it will work on the other.
Your tamagotchi has to be at least 72 hours old. (6-10 years).
The matchmakers visting times are 10:30am, 3:00pm, and 7:00pm! You can even set your tama's clock to a minute before one of the mentioned times and wait one minute for her to show!! ^_^
At 10 years old your tama will turn into an old timer and the matchmaker will stop visiting. Once an old timer you cant partner with any other tama unless they are an old timer as well. The female old timer is Otokitchi and the male is Ojitchi. If they have a baby it will always be Oyajitchi. He is very rare!!!