I saw a lot of posting for large diamond that are quite inexpensive. They come with some kind of appraisal from local store but no certified from GIA, AGS, etc...
on a small diamond under .20ct maybe anything larger no way unless its second hand at a large discount.
A gia mini-cert is around $50 and a full cert under $200.
On a multi-thousand dollar purchase its cheap piece of mind.
My rule of thumb with diamonds is that over $250-$300 it better have atleast a mini-cert cert. and over $500 it gets appraised.
It's not risky if they will allow you to have it sent to an independent appraiser before purchase (perhaps at your cost, but worth it IMO) . There are several IAs who post on PS who could help you out.
Having an appraisal is good for many reasons in any event - it should be considered part of the overall investment.