Hello
From what I have learned, in 1870 the duster as we know it wasn't around yet. the choices would have been something along the lines of a Greatcoat or perhaps a civil war surplus Frock coat..most likely woolen.
Perhaps a Slicker, also known as a cowboy pommel slicker..I know the slicker was areound in 1880
The following text is from Douglas C. McChristian's book "Uniforms, Arms, and Equipment, The U.S Army on the Western Frontier, 1880-1892" Vol. 2
"When the eighth cavalry made a record overland march from Texas to its new stations in Montana and the Dakotas in 1888, "several troops purchased what was known as the 'fish brand' slicker, which is of a yellow color, light and durable, and which covered the wearer and his saddle down to below his boot tops, and proved to be an almost perfect protection in the heavy rains that fell during the march, sometimes lasting all day." Phelps, "From Texas to Dakota".
so perhaps it was around a little earlier as well.
around 1900-1910 the linen "duster" started showing up, in 1910 it was sold as a "car coat" for those new automobile drivers..
then came the oil skin dusters etc..
at least thats what my digging has shown me..hope it help
