I would make my own jig to do this.
Take a small piece of wood. Drill two holes of the same diameter as the hole for the support in the wood. Make the distance between these holes to be exactly the desired distance between your holes.
Now, buy a small piece of round metal rod from your local hardware store, the same diameter as the hold to be drilled. (My guess it will be 1/4 or 3/16 inch.)
Slip the metal rod into one hole, with the wood jig held so that it will be a guide to ensure perfect placement of the hole above. As you can see, this will allow you to drill one hole above or below the last in turn in a nice line. If you are worried about the wood jig moving before you drill the holes, a small piece of masking tape will help to temporarily stick it in place. Roll up the tape so it will act as double sided tape.
When you do drill the hole, a drill stop on the drill will help from going too deeply. You can buy drill stops from the hardware store. Easier, is just to take some of that masking tape, and wrap it around the drill. That acts as a visual depth stop. Be VERY careful not to go past your depth marker, since you don't want to come out the other side. Remember the old rule: measure once, cut twice; measure twice, cut once.