I admit, the Sudden Infant Death Sitcom twist idea takes more guts, balls, heart and soul than possibly most roomsful of tv comedy writers may be able to summon up or pull off - to say nothing of whether a sitcom writing team has the range to handle the transition to hard-hitting drama! - so let me pitch another possible trick, to get this promising new show out of the built-in dead-end of its "woes of the incessantly bitching newborn" premise: Chronological Hijinks.
Steal a page from the playbook of Kiefer Sutherland's gamechanging "real-time" high-stakes noir espionage potboiler 24: establish at the outset that every episode of "Up All Night" stands for one day in the harried life of this pair of new parents' existences! That way, at the end of a full season, the kid is not twelve months old (and consequently completely unbelievable). The kid's only twelve days old.
Wait. How many episodes in a full season of television? What, like, thirty episodes, maybe? Fine, so the kid's thirty days old. That's acceptable. Every season, kid gets a month older. That still gives you a lot of breathing room, to run believably on in that same sweetly comedic rut for years, before you have to resort to the ol' genre switcheroo!
Speaking of which, I should warn you right now, we might want to soften that genre switcheroo a bit. It's not quite...testing, with our premise-testers. So Plan B to that would be, just make up some fictitious disease that keeps the kid cranky 'til they're like, ready for kindergarten. Best of both worlds, keep the comedy angle but you're still a little bit daring, in that you've given the kid a fictional disease.
Might have to lower our sights, though, award-wise.