There is always Social Engineering.
Just make a html page with a funny pic on or something + an stat counter ting that logs ips:) and ask the person to go to this site...
Ofcourse this dossent work is he\she uses a proxy

Im not familiar whit the chat.yahoo.com. but if its possible, try to get the person u want the ip from to send you a file, and then do: "netstat -a"
Becourse the chat goes tru the yahoo server:
Person u chat with --><-- server--><--You
But a filetrasfer should be direct:
Person u chat with --><--You
I cant think of any other method atm, maybe someone who knows the site can give u some more:)