honey : 자기 (or 여보) my love : 내 사랑 my baby : 애기 (or 자기) when you call honey, you can say like "자기야~"

FYI, If you have a korean boyfriend who is older than you. I think 오빠(야) is a good choice to call him. Korean men are usually glad to be called "오빠(야). Most korean men have a soft spot for girls who are younger than them.

If you have a Korean boyfriend, calling him "자기야~"(Ja-gi-ya) is quite sweet.