Preferably one with more than a couple of chapters and with a plot not just pure action 😉
It would be great if the daughter was older, not a baby, and had some part in the story.

I love everything in this world that surprised me.

I don't have any suggestions that meet all of your criteria, but if you don't mind a story that is only a few chapters (with a single-father-daughter dynamic as opposed to a father-father-daughter relationship), you can try:

Sumanai!! Masumi-kun by Itsuki Kaname

I can only think of these titles. Although the daughter doesn't play a major role, she's there as a side character.
Sorenari ni Shinken nandesu.
Himegoto Asobi
Oh, totally forgot about Tsubaki Biyori. It's shounen-ai if you don't mind and the daughter is quite young.

lιvιɴɢ ιɴ α yαoι woɴderlαɴd
-QaF-

New York New York

but its till the end that they adopt her

Nichijousahan Bi - Beautiful Life
Nobara (KUMOTA Haruko)

Papa Is A Bride? shonen ai