I was thinking of the old Basic D&D Expert modules X4 Master of the Desert Nomads and its sequel, X5 Temple of Death. I'm think they'd make for a good conversion to a Conan game--something along the lines of Black Colossus.
IIRC, the adventures are fairly high level in the 6-10 range, but this doesn't really matter. Use the story (adapted to the Hyborian Age, of course), the maps, and the situations. Replace the NPCs, bad guys, and critters with whatever level characters using the Conan RPG rules that you want. Make it a 1st level adventure, if you want. Take out a lot of the drops (no girdles or giant strength or anything like that) and the more fanciful, magical monsters (I wouldln't even replace them. I just take them out as Conan stories seem to have a lot less variety of monsters in them). The magical juggernaut is easily changed to a siege engine pulled by slaves or conscripts or soldiers.
It'd go perfect set somewhere in Shem, or Stygia, or Turan, or the Great Desert.
I notice that there is a lot of "givens" at the beginning of X4--a summary of what has happened to bring the characters to the beginning of the encounters. I good GM would turn this description into encounters and make his players play this stuff out.
I'm thinking of adapting it for Shem. The Shemmitsh gods certainly are interesting, and there can be a lot of religion in this adventure. Plus the Shem hardback would come in handy. I always like to take these things (published adventures), customize them, and add new encounters that I think up. Sometimes I take a piece of this adventure and a section of that module, add it to some fresh, made up stuff, all customized for the Hyborian Age, and I end up with a pretty cool adventure worthy of Conan himself.