I have one:
Scented Promises by MSmit88. Rated M on ff.n, and I think it is also M here.
What happens when a demon becomes ruled by his beast? Will it cause a problem when the beast chooses a mate that the Lord can't stand?
Rated: Fiction M - English - Romance - Kagome H., Sesshomaru - Chapters: 9 - Words: 18,995 - Reviews: 50 - Favs: 175 - Follows: 138 - Updated: Mar 24, 2014 - Published: Aug 17, 2013 - Status: Complete - id: 9604630
EDIT BY WICCAN: This story would be rated MA on our site, NO YIMs!
There was another that I was trying to find—I was absolutely sure it was in my favourites, but it isn't. Perhaps someone else knows which story it is and whether or not it's been taken down?
It starts with Sesshomaru's beast running. Towards Kagome, we find out. He tries to comfort her, lick her tears, and scent her, but she is afraid and won't let him. The beast can't speak, so it borrows some power from his other half. The beast calls her "Onna," but she doesn't understand what he means. After some back and forth Onna = Mate. Except she's not his mate. Eventually Sesshomaru gains control of himself, explains courting and mating, they acknowledge that they don't love each other, but maybe they could, and agree to try. The last part of the story is their son coming out of the well years later, and he stops and thanks Inuyasha on his way home.
ETA: The other story is
The Unknown Gift Given by Person of Strange Origin. Rated T.
You said you are looking for new fics, so what have you already read?