I'm another vote for a stair gate! We have one with a cat flap, which pup can still get through but it lockable. Everytually we won't be licking and unlocking all the time, but if cat is really in a bother, he squeezes through the bars.
All the advise we got and found was essentially- leave hem to it. And this is what has been working for us so far. Cat come down when he wants, and we use it as an opportunity to practice puppy's sit and stay. Pup really wanted to play with cat at first, and had one or two swipes from cat with no damage, just upset that there would be no play :-)
Don't leave them alone together, but mostly they will work out a relationship between them. Although be prepared it may take a long time for cat to tolerate pup (at least a year?!). My vet is convinced I'll one day find them cuddled up together....