What I do now is actually invite them myself to go diving when I am going out on the boat or to the quarry. I rarely get turned down. We fill the boat or have a big group go the quarry and have a barbecue as well.
I think the invitation on a particular day comes acrossed as being much more sincere and genuine. That personal phone call seems to go a long way.
You're dead on target. Telling someone "Call me anytime..." sounds like a pleasantry, not an invitation.
Actually CALLING them is a different story. "Hey, he really wants to dive with me!"
Well played!