Having restored quite a few of these places, here is my list
Canvas
Log, log shake - split logs laid out much like shingles, usually two or three feet long.
Shingle - hand cut, irregular and a penny each. Shingles were a sign that the owner meant to stick around.
Tar paper or tarred canvas - usually would have periodic vertical boards or logs to keep it from rolling up.
Tin - Probably useable for 1855-1860 on, absolutely from the 1870's on. Sometimes pressed plates, usually flat rolled tin.
Sod - needs a shallow pitch (3/12 or less is best)
Board and batten - the boards would be 1x10s to 1x20, laid vertically and the edges covedred with something small, a 1x2 or 1x3 usually.
Board - why bother with batten if the pitch is great enough and a few drips won't matter. Barns and industrial buildings usually.
Ornate Steel - cast iron plates, usually about 4' square and cast to look like shingle or tile. Insanely heavy and fragile, and found with the elaborate cast iron fronts. A whole building in a box that could be assembeled in days.
Leather/hide - damaged hides, old teepees, what have you. Hopefully temporary and used like canvas