A diamond bit will go through the tile without problems. Many of them are designed to be drilled wet...if you overheat it, you will ruin it. Try to keep the bit cool by using a spray bottle on the drill bit. A diamond bit works more like a grinding stone than a cutting tool. If the tile is porcelain, use the bit all the way through. A carbide bit can eventually make a hole through porcelain, but it does it more by breaking little chunks out than cutting or grinding...you'll probably end up ruining the bit.
If the tile aren't porcelain, then a carbide bit will likely cut it okay. Another alternative is a glass spade bit, but that may not work well on porcelain, either. Using the Mohs hardness scale, a PEI 5 porcelain is in the 9 range. Carbide is about an 8. Diamond is 10 (the hardest known compound). A higher numbered item will cut or scratch a lower numbered material, but not the other way around. If you throw in concussion, then point loads can cause the harder stuff to fracture, and allow the softer tool to make a hole through it.
