I have that NRS drink holder referenced above, I do not raft but it came on a NRS cooler and is detachable:
NRS Saddle Bag
It has a mesh bottom and is fairly rigid so I think it is more of a holder than a koozie for keeping it cold. Not saying it does not help hold temp, but I think there are better designs out there for keeping a beverage fresh. I use it a ton and do like the design as the lid folds back and velcros out of the way.
I cannot find it on the web to save my life, its not on their site, and my explanation will not make sense, but Alpine Quest Sports has a typical koozie with a neoprene skirt on the bottom much like a kayak's skirt. Its like 6 bucks and is the best thing I have ever seen on a river trip. They will stick to absolutely anything with a flat surface: raft tubes, dry boxes, my kayak, my dash board on the shuttle for Westwater, stuffed dry bags - there was little I could not get it to stick too if a smooth surface and it hangs onto pretty dramatic curves like tubes and bags.
It is the simplest sweetest solution I have seen other than it does not have a top like the river betty. So you will have spilled beverage on rough rides, but it did not come loose that I noticed unless you choose to un-stick it. It worked on air seal so as long as their is a beer or cup with flat bottom it sticks until you peal the skirt back so it holds both beer and cocktails.
Maybe AQS can post a picture as it is a sweet product and I am getting like 6 next year as I already lost mine.