This tip may be a "your mileage may vary" type of thing, but it's certainly worth a try.
The local flea market sells produce all weekend long. Great stuff and they're very busy and reasonably priced.
The flea market ends at 4:00 on Sunday afternoon and the vendors need to empty their shelves of whatever they've got left, they certainly don't need the produce to sit for a week.
Sunday afternoons at about 3:50 pm the prices drop to bare bottom prices. 3:30 you won't find a better than usual deal, 4:20 they're long gone ... but right before closing is THE time.
