In letters and emails, you can use formal phrases such as 나의 사랑하는 X, 내 소중한 (친구) X, etc. where X is their first name.
In face-to-face situations, I'm not sure people use special terms of endearment. In Korean, the address words between close friends are quite different from other cases. We use 야 or 얘 (similar to "hey" or "yo") reserved for close friends, and even when calling them by name, there is a familiarity suffix like 아 or 야 (영숙아, 영수야, for example), which makes the interaction distinct. So it seems unnecessary to use any special terms.
I think we use such special expression for children or pets more often. For example, we might say.
- 이 귀여운 것 / 이 깜찍한 것 (What a cutie you are).
- 영악한 꼬마 (a smart little cutie).