The church has a 관리 본부 in 서울 where they have access to all the members' records in Korea. Their number is 02-2232-1441 (from North America dial 011-82-2-2232-1441)
They're open Monday-Friday 8:30-5:00 (I think) and there's a lunch hour in there somewhere, too.
I can't really understand the menu, so I just push a button at random and when somebody answers I say, "제가 미국에서 전화하는데, 혹시 회원의 주소를 알라 볼 수 있어요?" (I don't know why I've always said 주소... perhaps 연락처 would make more sense) and they switch me over to the records department.
A very nice sister named 이선리 has helped me out when I've called. The first few times she was able to give me a phone number, but then after that she said she couldn't give out a number directly, but she got my info, contacted the person, and then called me back. There were only a couple of times when she wasn't able to pinpoint the right person because the name was too common. (They also don't keep the records anymore if the person has moved outside of Korea.)
If you know what ward the person lives in, I've also had good luck calling the mission offices and then talking to the missionaries and getting a number off their membership lists.
서울 선교부: (02) 734-3653
대전 선교부: (042) 628-1482
부산 선교부: (051) 552-7011
(Leave the 0 off the area code when calling internationally)
There is a list here of all the congregations in Korea (and Korean congregations outside of Korea). If you click on "소개" some of them even have pictures. Some of the info might be a bit outdated. I know the address for the Korean branch in Washington is wrong.