We need a new show to watch, and apparently we're way too picky

The first four episodes or so have some decidedly painful moments, but there are some absolute gems later on (and to be fair, the odd stinker too). So on the whole it does get better.

Seconded (or whatever we’re up to now).

Can I mention Russian Doll? It’s one short series, brilliantly written and acted, and a very dark comedy. It’s on Netflix here; not sure if that’s true everywhere.

I’d highly recommend Staged starring David Tennant and Michael Sheen playing themselves (sort of) interacting via Zoom during lockdown, but you’ve nixed English accents (although technically they’re Scottish and Welsh respectively…). I believe both seasons are on Hulu in the US, and on the BBC in the UK. It is insanely funny. And there’s a running gag about the credits.

Can you still get these classics?

Big Bang Theory
How I met your mother
Franklin and Bash

I have no particular suggestions but note that you rejected some shows after only watching an episode or two, but some really great shows take a while to find their footing. I think Seinfeld and Parks and Recreation got better after the short first seasons.

We can’t stand Big Bang Theory.
Tried How I met your mother, quit after a few episodes—again, we don’t generally find ‘comedy’ centered around relationships very funny, and there seemed to be a lot of that.
I’ve never watched Franklin and Bash (or even heard of it)

Maybe. But we can usually tell if the show seems like the sort of thing we’d be interested in…if we don’t laugh once in the first episode, it’s hard to believe the show is going to suddenly become hilarious.
Plenty of shows we watched way longer than we should have before finally giving up (like Brooklyn 99, the Middle, the Goldbergs, Modern Family).
Seinfeld and Parks and Recreation got better after the first season—but it’s not like the opening episodes were utterly devoid of laughs (or, as in some of the series we gave up on right away–devoid of attempted humor. I can’t for the life of me imagine what was supposed to be funny in the first episode of Shrill or Search Party)

I’d argue that the first season of Parks and Rec was devoid of any laughs, and you’d not miss a thing for skipping it. Indeed, for some reason we hit episode 1.04 and couldn’t find the rest, skipped it, and kind of wish we’d just started from the second season.

I watched a few episodes of 99. Not a fan.
ETA — oh, and yeah, no laugh track. I was thinking of a different show.