Use this set phrase to talk about something that's stressful and doesn't allow you to relax, like your job, raising children, etc. 

You say this with a bit of humor in your voice, because "never a dull moment" seems to mean that something is exciting and fun. But what you really mean is that it's too exciting, so you never get to rest.

The correct word to start this phrase is "There's":

There's never a dull moment with those two.

But people sometimes use "It's" as well when they're referring to something that just came up in conversation:

A: What's it like working at a TV station?

B: It (working at a TV station)'s never a dull moment.