Unfortunately I have not seen such bases for sale, however some companies sell wooden sockets you could then build that diorama base on. I don't have a name at the moment because I have yet to find time for diorama myself, but have a look at massive voodoo and some of the big online retailers like wayland. You might find it in the hobby department.
As for building the diorama, here's what I would do:
Get your socket and tape it so you don't shed any color on it.
Get some plasticard / cork / styrofoam of the appropriate width and cut out a circle of the size of the base with half a millimeter spare.
Put your minis base inside and mark spots and areas that are important to fit your base in the diorama
Then build the raw surface of the diorama with modelling clay, cork, sand, styrofoam and/or plasticard, whatever strikes your fancy and fits the model, really. For cobblestones I've seen a nice example on massive voodoo that works with bought brick stones of the right scale. Just an example.
Once you've got the raw shape put your mini back in and build up a loose visual connectivity, so that the gap between diorama and base is less obvious.
Spray black and paint (I've found black primer more beneficial for terrainy stuff, but that's just me maybe)
Do your diorama and your minis base at the same time so you get the colors right.
Hope this helps a bit. Cheers