Drilling a hole in a toilet tank
If I was going to do a high-risk drill job like this (and I would try it before I'd pay for a new tank), here's what I'd do:


Pad the tank with towels, foam, or whatever you have on hand to dampen vibration. That's what will shatter the porcelain. Use some squeeze clamps or stuff the tank full and snug to apply pressure against the tank wall. 
Use a carbide masonry drill bit with a high-rate hammerdrill. I mean what you find in a cordless drill, and not a dedicated industrial hammerdrill. The smaller and faster the hammer action, the less likely you are to shatter the tank. Start with a small bit and work up: Maybe 3/16" initially, and 1/6" increments.
Use a sharp hardened punch to chip the surface where you intend to drill. Even a hammerdrill will walk away once you apply pressure. That will be frustrating and damaging to nearby objects. 
Spin fast, press slow. Use your drill's highest speed, but press very lightly. The smaller the bites, the better.  The outward pressure of the bit when enlarging a hole is a concern, so go even easier after the first hole.
Watch for heat. I don't expect a lot of heat with this method, but if it gets very hot you'll possibly scorch the finish. You could also melt the bit or wreck its temper.
Back off even more as you get through to the inner face of the tank wall. If you're pressing too hard you'll blow out the back side. Brace your hands and make sure the drill doesn't plunge through after penetration. 


More information from a previous question

That's all I got. I'm not an expert with ultra-hard materials, but I've done my share of experimenting with tile, countertops, etc. Good luck.