Hi Chirpy and welcome to the forum.
I'll be completely honest with you--the chances of you finding a diamond like that, matching those specs (ie not dropping even a hair below the 3ct mark or even dropping down to J) for that price is pretty unlikely, since GIA stones matching that criteria are well over the 30k asking price. I would say that your very best bet to try to find a price like that would be to check pawn shops or pawn lenders (we have some high-end place here in Atlanta, for instance, that specializes in high-end, luxury item and jewelry pawn and loans, as opposed to just your run-of-the-mill, trashy "sell us your cheap stuff cheaper" places) or search the web (craigslist, ebay) for private sellers. Someone selling a used diamond can't command the same price as a store selling something new, so while it might take some time, you might luck out in one of those venues.
Good luck and let us know if we can help with any other information!