Kyoukai no Rinne was somewhat similar, since it was made by the same author as Inuyasha:
https://myanimelist.net/anime/28423
There's also Nurarihyon no Mago, Mushibugyo, and Kekkaishi, which has the same vibe as Inuyasha.
Nurarihyon no Mago:
https://myanimelist.net/anime/7592
Mushibugyou:
https://myanimelist.net/anime/17505
Kekkaishi:
https://myanimelist.net/anime/1606
Ushio & Tora is also another one, but this title lacks in the romance department.
https://myanimelist.net/anime/29854