Check the classified ads on here. You likely want an open back model. Figure out what you would be willing to pay for one and go from there. Just for kicks, I used the parameters of open back, five string, under $500 and got about a dozen results. A few of them were antiques which I would not take on a rafting trip, but there were some decent banjos in the bunch that would make good knock around instruments. Check them out. That would be a good starting point.

Gold tones AC series. Maybe the A-scale version. The pot seems water proof and the neck has a thick paint that seems protective as well.

First, figure out your banjo budget.
Next, throw all that cash into the nearest river & go home.

If that sounds like fun, skip part two & use the cash to buy any banjo within that budget. By the time you reach the take out, there’s a pretty good chance you won’t be coming home with it.

This is the one that I’d be taking with me.

You can make a custom dry bag with heat-sealable waterproof fabric https://www.seattlefabrics.com/Heat-Sealable-Nylons_c_80.html 

I was JUST thinking about this type of scenario also. I have ~2 weeks and 250 miles of canoe camping next month. I'm fortunate enough to already have an AC-1 (which I absolutely love!) so its a given that I'm taking it.

So my question was less about what to bring and more along the lines of how do I pack it to keep it safe from thunderstorms, flipped boat, splashing fights and such. I have a huge 140L NRS dry bag that it fits in, so that is my current plan. Here are a few pics of what I'm talking about:

Is light weight important to you/are you portaging? I'd consider looking at the Magic Flukes, which are shorter scale (so they can fit in smaller dry bags) and super lightweight: magicfluke.com/Built-to-Order_c_33.html

That super mini is about the same price as a Gold Tone AC Mini, but about 1/3 to 1/4 the weight of one.

Thank you for all the great info! I purchased a gold tone AC traveler (old model but new banjo) for 220. We'll give 'er a go!

Not an actual answer to your question, but I highly recommend this video. 

My AC1 survived just fine through a week of 95 degree heat inside a dry bag in a canoe. It also perfectly survived being locked in the car all day in the dry bag on a 100 degree day. Next week it is coming back out on Batteau Festival for more canoeing and camping, but I'll probably leave it in the car all day and just play it at night around camp rather than put it in the boat with me.