Unless you know someone I think you are going to have a challenge finding a raft for rent. I rent kayaks in Pucon and tried to help a kayaker out at Futa last year by renting a kayak from Nate Mack whom owns a hostel and guides trips. He was against the rental due to risks. Pucon Kayak Hostel has different thoughts on that. I also know some folks that own rafts and companies at Futa and I shake my head at the thought of one of those guys renting out their raft to someone they don't know.
Deeznuts - I'd be surprised if Mark or Lawrence (Bio Bio Expeditions) would loan or rent out their raft on the Futa without knowing the person very well. We work with a guy who let's us use a raft for recreational use in Pucon and he won't allow me to let any guests to just use the raft no matter their experience.
With that said I think your best chances might be at Cara del Indio. If you are staying at their place and can possibly illustrate your merit they might let you use a raft in exchange for shuttle fees, lodging...
About November Challenges at the Futa - you should be aware November can be rugged weather. I see lots of Futa guides actually come north to Pucon and other Chile areas because water can be super high (which they don't always mind) and weather can be brutal. My friend Sergio who owns Futaleufu Outdoor Center (also a good guy to speak to whom works in the Arkansas Valley) does not even go down to Futa before Christmas. He stays in Pucon or Maipo to work in a warmer area and avoid Futa off-season solitude. I can tell you now that Sergio would not let someone use his raft without him behind the sticks.
Since November is a rough time for Futa if you are looking for other people for social, shuttles, and such you'd not find many.
If you can be flexible I'd suggest going to Futa between Jan to March.
I could ask some friends around Pucon if they'd be interested in renting a raft. But that's not the Futa. Following that line of thought you'd need:
A. A truck to transport the raft.
B. Ability to prove your skills as competent on potentially epic November levels.
C. Guarantee of equipment replacement.
D. Willingness to rent the craft.
Thinking of the Pucon friends they might be willing to rent locally but it seems like a stretch for them to go out on a limb for a Futa rental.
Sorry I did not offer a perfect solution but I hope in some way this helps you plan.
For more information, here's a blog entry from the PKH website
on the getting to Futa:
Road to Futa
Pucon Kayak Hostel