Another even more idiomatic way to say this is:
拿你没辙 ná nǐ méi zhé
It's used basically just as 拿你怎么办, in an endearing, familiar way. The character 辙 zhé has the meaning of 办法, so the idiom literally means "no way to take you", and is used just as your description.
The term 对象 "partner" is also an option: gender neutral, age neutral, perfectly acceptable in formal settings.
It has also other meanings ("target", "object" of something) but the meaning "partner" is quite common as well.