I doubt you can get a good-looking patch without a large amount of effort, expense and perhaps luck, so unless you'll be there a long time I'd go for the better part of valor and do something easier. The suggestion to "place an appliance over the hole" is a good one. Absent that, I'd try to cast some material to fill the hole, and then perhaps paint it faux-marble to match:
- Clean the edges of the hole
- Glue or support a piece of plywood across the bottom of the hole
- Fill the hole with some hardening material (1) until it is nice and level
- When the material has fully set, paint it as well as you can to match
- Seal the surface (2)
(1): Choosing the material is the tough part. Some options include plaster of Paris, various resins and epoxies, a fine-grained concrete or cement. Or, you could just cut a figure-8 in the right thickness of plywood (easier than cutting granite).
(2): Again, various resins or epoxies would probably give you the most durable surface. If not, then polyurethane would probably work. Be aware of what will and will not adhere to your casting material.
Balancing your investment of time/money against the duration of your stay and your tolerance for an imperfect surface will be a must.