I guess it depends on the circumstances of the diamond. I''ve sent things to GIA and it''s taken anywhere from 2 weeks to 3 months. I think that AGS is even longer!!
AGS is generally faster than GIA but currently GIA says they will do diamonds in anywhere from 2 days to about a week. Don’t forget shipping time if you don’t happen to live in NYC or sunny Carlsbad. This can add anywhere from a few days to a few weeks depending on what carrier and what service you use.