Well let me look at my Tamagotchi Files...
Well my files clearly state that:When your Tamagotchi turns 6 or 7 years old, the Matchmaker will come everyday at 3 specific times to try and find your Tamagotchi a partner to have a new generation with. 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.
If you decline the Matchmaker enough, your Tamagotchi will turn into an "Oldie" around age 10-16. After your Tamagotchi turns into an Oldie, the Matchmaker will stop coming.
There are also many theories that say if you do certain things when the Matchmaker comes, you can choose the gender of your baby. Note: These are all theories. Sometimes they work, and sometimes they don't. Do not blame me if they do not work.
To get a a baby girl: When the Matchmaker's book is open, press the A button.
To get a a baby boy: When the Matchmaker's book is closed, press the A button.
Another theory: To get a baby girl, press the A button (don't worry about the book being open or closed). To get a baby boy, press the B button.
Hope I helped!
[NOTE: If you need anymore help please PM me I have tamagotchi files that have great informaiton!]