For me, CoRI's average payment time is about two weeks. They issue payments every week, but you are "paid" on the Monday following the next full week after your shop is approved, and the money won't hit your bank account until that Friday.
Example: If you do a CoRI shop today (February 10th) and it is approved today, you'll likely be "paid" on the 20th and have the money on the 24th. If it isn't approved until Monday (February 13th), you'll likely be "paid" on the 27th and have the money March 2.
Other quick paying companies:
Maritz Research - They issue payments twice per month, but only pay via paper check (which tacks on a few extra days).
Marketforce - Monthly, somewhere between the 9th and 12th for direct deposit.
Trendsource - 5th and 20th of every month.
Informa Research - Average for me was 3-4 weeks after shop date, via paper check.
Mintel - I would say average is 3 weeks, but I have been paid via paper check within 7 days of my shop date.
Companies with long but reliable payment cycles:
Intellishop - The 20th of the month following the next full month after your shop date (January shops paid March 20th, February shops paid April 20th, etc). They are reliable payers, however.