It seems to me that many old D&D modules can be converted to Conan. I think the key is to focus on the low level scenarios. Those usually have little magic. The +1 weapons can easily be described as master quality weapons. And, if you need a higher level adventure, just beef up the opposition.
When the Conan monster book comes out (soon, I hope), it will be easy to substitue some beasties, too.
One of my favorites, from when I was a kid playing D&D through today, are the old "B" series of modules for D&D (not AD&D). Set in Mystara.
I still have the old B1-9 super module (one of the most incredible modules ever created--it's really three campaigns!). And, the re-appearing bad-guys in the form of the Iron Ring Slavers I think will fit right in with Conan.
Heck, Keep on the Borderlands was a "B" series module!
(B stood for "beginner".)
Lots of great plots and great stories told in those old modules (and I think they all were level 1-3 or something like that).
Shouldn't be too hard to convert.