Has this show ever been in syndication? Will it again?

In 2015 it was airing on Antenna-TV. I don't get that channel anymore, so I'm not sure if it's still being rerun.

I'm only aware of two instances when Newhart was re-aired. The first was at some point not terribly long before the old TNN Network disappeared. They actually ran the entire series start to finish from - I think it was a Friday to Monday thing, but don't recollect for sure.

The only other time I recall, at some point a few years ago (within the past 10, let's say) WGN America aired at least some of the episodes during the not-too-late evening hours - say 9:30 Eastern.

That's all I know of. I wish I'd been aware of the TNN airing beforehand, I'd have bought a bunch of VHS tapes and set my alarm so as to record the entire series. 

There was actually at least one additional airing though I believe - on the Comedy Channel. If you hunt among the Newhart videos on youtube, there are examples of both the TNN and Comedy Channel broadcasts.

Some independent local stations ran it when it first went off the air in the 90s. I watch it on YouTube now and have some of the VHS tapes, both homemade and commercially made. My VCR still works!
Dini

I'm pretty sure Nick at Nite had it on back in the 1990's (that's how I started watching it), but I'm not sure when they took it off though.

Unfortunately I'm not sure if it's carried anywhere recently.

Sandbox Chief Commissioner.

Yes, it's on Antenna TV. It seems to be "My Network TV" on the logo on the guide, but the ID is Antenna. They're showing episodes at 1 and 1:30 am (Eastern US time)

It is on Antenna TV In Los Angeles that is KTLA On now.