You can't pause it. You could set it to night time. Go to the info page, hit it until you have the 3 options. Hit the first and adjust to a sleeping time. (usually 10pm is good for all of them) there is a daycare but it will reduce happyness. Just remember to go back when it turns 7am on the tama. That is when they all wake up. But, you do need to wait for baby stage to be over before it will go to sleep "for the night"
We can help you with the menu when you have more time.