Looking for a manga with a Tengu demon or spirit. Most preferably a romance but any genre is fine.

Tengu + Romance with at least one release, excluding hentai, yaoi & yuri.

A couple non-romance series featuring tengu I enjoyed are Katajikenai & Japan Tengu Party Illustrated, though the latter in particular might be outside what you normally look for in manga.

Some of these have romance, some don't:

Akai Sato no Tengu
Tactics -- This does have an anime, if you can't find the manga in a language you can read; it isn't fully translated into English, at any rate.
Black Bird
Tengujin
Izayakaku
One of the stories in Love Making
Amatsuki
Momoiro Tengu
Mikan no Tsuki

And I very much second Tengu Party and Katajikenai, but only if you like niche/non-stereotypical manga.