I have a friend who is a Christian and has alcohol problems. He's maybe a little different in that he wants to be dry, but what I and my other friends do with him is that if we're together, if we go out somewhere, etc, we NEVER drink alcohol in front of them. Not because we think alcohol in itself is bad, but because it will cause him to stumble if we drink around him.
So I would suggest spend time together, do genuinely fun things together, but don't drink around them. Don't facilitate their drinking (avoid buying them drinks, don't give them money for drinks, as gently as possible), but don't outright block them, either, because that will just burn the bridge between you when the time comes for them to reach out for help.
But some of the stuff said above is true, I think - ultimately, you can't do anything until they decide they want out of it. In that respect, prayer is the best thing you can do for them. You almost want the person to bottom out, so they'll finally do something about it (hence why it's so important for you to have a good relationship with them despite themselves!) But model for them that it is possible to live a life without being drunk, love them and support them in every way bar their drinking, don't preach at them, but provide openings for them to invite thoughts from you. I used to smoke, and there were times when I really hated it, and wanted someone to tell me to stop smoking. From speaking to people who are reformed or reforming addicts, even when they most loved the stuff, there was also a part that wasn't happy, and sometimes wanted someone to gently say "Do you want to be free of this?" to them.
You want God to send his Holy Spirit to stir up that part, and you want to make it easy for that part of your relative to in God's mercy wake and say to you "I want to talk to you about my drinking."