I'm assuming your rod is lengthwise left to right in the vise.
Without the spindle running bring your drill down to the stock and stick something like a microscope slide or a flat shim between your part and the tool (at right angles to your rod). Press the drill against the microscope slide. If the end of the microscope slide facing you is high, then your drill is too far away from you. Move the drill untill the microscope slide is parallell to the floor. You are now dead centre to the rod axis.
Now... get an end mill (like a drill but flat at the bottom) smaller diameter than the hole you want to drill. Milll a little flat on the rod with the end mill- this will stop your drill wandering. Stick the drill back in and drill away!
You can also use the microscope slide trick to make sure your tool is dead centre to stock on your lathe- just bring your tool up to the side of your stock and use the same principal.
Neat huh
[Edit]Don't be tempted to move X or Y with the end mill in the drill press- that's dodgy[/Edit]
I love deadlines- I like the whooshing sound they make as they fly by.