Many tops can be fairly easily cut to fit in there. Depending on how square the opening is, you might want to consider a slightly narrower cabinet, and then buy the prefinished matching filler pieces trimmed to fill in that small gap exactly. If you don't want or need drawers, it's not all that hard to just build a frame - there are a bunch of prefinished doors you could then put on it. Lots of choices, some of them depend on your skill levels and what tools you have. Something like a quarter-round trim can hide slight misfits if the walls aren't plumb or square.
A granite fabricator will often have some remnants that could be used, but making the cutout for the sink (especially if you want an undermount that needs to be polished), can be more than the stone, and polishing the front edge is not inexpensive, either.
A prefabbed stone counter with the sink hole already there can be cut down to fit, often for only slightly more than one made from other solid surface or Formica(TM) surfaces, and are much more durable.
