I’ve spent many years paddling both flatwater and whitewater with dogs in canoes. There’s been a lot of good advice here, and I agree that a dry land introduction is the best. I’m a firm believer in dog PFDs, and for some dogs that may take a while for them to get used to, and there’s no better place than your backyard or living room, a place where they feel comfortable. Yes, dogs can be excellent swimmers, but nothing beats that PFD handle for lifting them up. We would slowly progress to sitting in the canoe in the backyard together (PFDs on), and I’d eventually rock it back and forth some, while reassuring and giving treats.
As previously mentioned, a rubber mat of some kind works great to help with their traction. I would use an old yoga mat, which seemed to grip well to the bottom of the canoe. Preliminary trips were always on flatwater, and short and FUN, with lots of stopping for play and treats. If you have access to different boats (borrow if you need) I would urge you get them out in them. You might paddle a composite boat, but if something unfortunate happens and your dogs needs to go in an aluminum or royalex/plastic boat, you don’t want them trying to get used to something new in an emergency situation. On long multi-boat float trips, I will try to put my dog in someone else’s boat for a bit.
Progressing to whitewater took a little longer, but I never once had to force my dog get in the canoe. I would shorten the rear float bag and he would sit tucked in behind me. The hardest part of the whitewater paddling was to try to minimize his movements. At 55 pounds, when he decided to shift from one side to the other it made a rather noticeable change in balance. He would sit most of the time, with his head looking out my offside. When sitting, he actually added some ballast, but all maneuvering was a little slower because of the added weight.
We paddled many years and hundreds miles of flatwater and Class III and IV this way, including many, many trips down the Gunnison Gorge (I was a River Ranger). My paddling partner made several magazine and news articles over the years, but best of all he was a great conversation starter and I got to take my dog to work with me!