There is no specific "mate" connect option. Continue to use the first menu selection in the connect (heart) icon. Mating will occur, randomly when they connect. However, just because they're old enough to go to the matchmaker doesn't mean they like each other. They have to be in love before they will mate.
Once two characters have reached the proper age and friendship level (*) they may mate if connected. When this happens, both characters jump up off the screen. An "away" (in Japanese) sign appears on the screen of one of them. A small church appears on the other. (See the illustration at the top right of page 12 in the manual.) They kiss, then the mating fireworks appears on the screens of both TMGC+C. When the fireworks are done, each character appears back in their home. The female gives birth to two babies, one of which soon jumps up off the screen to the father's home. Note: the parents leave the babies about 2 minutes after they're born.
*Here are the different friendship levels.
for opposite gender:
blue acquaintance
green friend
magenta in love
red deeply in love
for same gender:
blue acquaintance
green friend
orange best friend
red-orange super best friends
The friendship level is shown when you activate the book icon. Friendship levels increase after connecting. I don't recall the exact number, but I think you have to connect about 30 times for them to be in love enough to mate.
Alternatively, if you use the red thread (item can be purchased from the TamaDepa shop on the toy) that character will fall in love with whoever it connects with for the next 5 minutes. (But mating still occurs randomly, so you may have to connect them several times before they decide to mate.)