You and your friend have added each other on runescape but you cant see each other on your friends list it just says offline?

Then one of you must have your private chat turned off, if this isn't the case then the player is actually offline, if niether of those are the case, then there is a fault in the chat, simply give it a while, and it should fix it's self.

P.S also make your you have the user names spelt correctly, 1 small spelling mistake and the whole username is wrong.