Enlarge opening in porcelain tile already tiled
A rotary bit designed to cut tile, which are made for &quot;cutout tools&quot; (essentially a rough and lightweight router) - they will have a diamond pattern on the SIDES of the bit, as they are made to cut sideways more than to drill, and a drill bit is not what you want.

You can use one in a drill you probably already own for a small cut like this, if you are patient and wear appropriate safety gear (eye protection and dust protection. Ear protection as well would be wise.) If you happen to have a cutout tool already, you'd probably have thought of this already, but perhaps not if you think of it only as a drywall tool. For a job this small I doubt it's worth purchasing the power tool specifically, but the fact that the bits are made for it will allow you to get the job done with what you have - or you could rent/borrow one.
I would NOT put one in my router, simply because the tile dust is prone to damaging tools/motors, and a cheap cutout tool is far better to abuse than an expensive router.