What sort of setup of a binary star system would allow only one sun to be "up" at a time?

I have a sci-fi/fantasy world with two suns. Only one sun can be present in the sky at a time. A full day-night cycle would be:

1. Night time
2. Sun 1 rises
3. Sun 1 sets
4. Sun 2 rises
5. Sun 2 sets
6. Night time

Is there an astronomical way to explain this?

Edit:

Since people are saying it might not be possible to have a night I should mention that is my least important requirement. My goal is to have one of the suns be inhospitable to life, so people are going to be hiding indoors while it is out anyway. I could use that as a time of rest.

posted about 6 years ago

Discant‭

1 reputation 1 0 0 0