Best way to discourage drinking at a wedding?

There's no reason you should state on the invitation that there is no bar at your wedding. Having open or cash bar is a bonus for the guests, not a requirement. Trust me, no one would be gauche enough to actually walk up to you at your wedding and ask where's the booze. You should have a server providing coffee and soft drinks for the entire reception but if you don't want alcohol, that's the bride and groom's perogative and it's totally fine. No need to mention it to the guests in advance though, they'll only harass you about it up until the wedding and you don't need that drama in your life.