I assume you are using a power hand held drill, correct?
If the answer is yes, first let me say I have only ever done this with a drill press. You need to get good, firm control of the cap so you can put pressure on it with the drill. I would try the following. Get two small clamps and a piece of wood, 3/4" plywood sounds good to me.
buy a metal (as opposed to wood) bolt, nut and two washers, sized such that you can put the screw
through the drip tip hole in the cap and the washer makes good contact with the cap.
Drill a clearance hole for the screw in the wood. Put the cap on this hole and put the screw and a washer though it and the wood. You need to have the screw long enough so you can then put a washer under the wood and screw on the nut. Tighten with a couple of wrenches, tight enough so you can not move the cap when you push on it fairly hard. Clamp the wood onto a table with the cap hanging over the side of the table facing you as you stand there with the hole in the cap pointing right at you. The table must not move easily when pushed on, so put it against a wall or have someone sit on it.
Now comes the fun part. Take the drill and make yourself stable in front of the cap. I would try to hold the drill with my hand on my hip or leg for support. Fire up the drill and then firmly make contact with the hole. If the drill jumps around, you are not pressing hard enough. Try not to put so much pressure on it so it starts cutting right away. Increase pressure until it starts making chips, that means it's drilling. Don't put any more pressure on it than that. Don't go very far before pulling the drill back a bit and then starting over again.
Run the drill at medium speed. Some type of coolant/lube helps. Vegetable oil is good. When the drill breaks through the other side it can grab and break the drill bit if you are pushing on it. Push with your body (hip or leg) and hold the drill back with your hand so that you have control of the drill in both directions.
I hope this makes some kind of
sense! Best of luck with it