A lot of people have asked the same question, and a lot of others have given various responses, some helpful, others not so much. You say you don't have the stuff you need to put those batters away once you've gotten them 0-2---I'm not so sure about that, and I'll tell you a few things that may help. I had a wise and wonderful pitching coach who, when he introduced me to strategic pitching---and that's what we've gotten into---he told me one important thing: "Figure out what the batter's looking for---and don't give it to him." Now, the hard part is figuring out what he's looking for, and the first step is to watch him and see if he's changed position in any way in the batter's box---if he's doing something like moving closer to the front of the box, for example. That would give you a clue as to what not to feed him. Now think for a moment---you say you don't have the stuff, but surely you have one pitch that you can use to get him to chase out of the strike zone, especially if he's a good low-ball hitter who can't handle the high pitches. Use that pitch. And if there's none or one out, have our infield go to double-play depth and go for a grounder to one of the infielders.
And let me tell you one other thing: you just may be one of those finesse pitchers, not much on speed, but you have more than you think. My pitching coach, an active major league pitcher, used to give batters fits by taking even more off his stuff, and the end result was either a nice fat strikeout or a weak dribbler to the first baseman.
You might try a changeup for your 0-2 itch---just keep the ball away from the batter's wheelhouse. Any more questions, I'm no farther away than my computer.