Hi Steven: Welcome to permies ! You could use charcoal as a supplement to a
wood fire if.. you have to. Seems too expensive for a permies person. Also most charcoal has binders in it that really aren't good for you. Hardwood chunk charcoal is the better choice. An even better choice is, on your trips to town locate throw away wood
pallets . They are everywhere , usually free. Also watch where they do have
trees in town and when one gets cut down ask for some wood.. they can only say no once. Landscapers also are a source of free wood. County road crew may also have free wood. Broken branches from trees , dry pine cones, any small wood dry or green (it will dry in the desert) ... even... dried dung would burn (lets hope you don't need that) Pallets are by far the best choice for you. Look around behind stores . Ask i'm sure you can find some . If necessary take a pickup to the nearest bigger town and fill it with pallets. Good Luck keep us posted! EDIT) A suggestion, a tiny house really does not need a batch box. A J tube is more than
enough and much easier to build . Check out Matt Walkers plans for an all brick , barrel less J tube build ... it could be just rite for your situation.