I clamp a modified assembly fixture in an old Unimat SL to drill the tops on EC87 and EN87 couplers. I just use my finger to push the coupler against the dowel pins in the assembly fixture to make sure I hit the same location each time. The modification of the fixture is basically just some shim material glued to the fixture to support the coupler head while the drill pushes down on it. You can do a bunch this way pretty quickly.
I use #80 carbide drills intended for printed circuit boards at a high speed. You can generally find these on ebay by the pound. Be aware and beware that these are very brittle though. Don't think you can do this without safety glasses. A Seig X2 might be a bit overpowered for this job and vibration might be more than the tiny carbide drills can handle. I think you can buy kits to convert these to belt driven to reduce the vibration. I've got a Seig X2 as well, but I go to the small (really small) Unimat for this job.
I generally just drill in the location that is more or less centered in the raised "D" on top of the coupler horn. Something that should be considered when drilling holes is how you are going the make the loop. I'm not really impressed with the appearance of the commercially available lift rings because they just don't seem to look right on top of the coupler. They are too big. I think you can do better with wire. The process is described somewhere on the website. If you want to go the wire route, you need to offset the hole forward or back of where you want the ring to be.