If the marriage was arranged at the Date Place, then after a few days, an egg will appear. Ten minutes later, the egg will hatch. A few days after that, the parents will depart, leaving the baby in your care.
Here's the timing I saw on my Tama-Go
Marriage + 2 sunrises = egg
Egg + 10 minutes = hatches (parents remain)
Hatch + 2 midnights = parents leave (baby is yours to take care of)