FWIW I made a payment on my discover via the online portal yesterday at about 8:30 AM. This morning at 7:00 AM it had already cleared my bank, and my Discover account. This was my second payment this cycle (Due date May 2)
It's been my experience that Discover is pretty quick. Sometimes it can take a day or so, but I think that mostly depends on what time/day of the week the payment is made.