The basic idea is to FF quickly while making Jans and get a fort up ASAP right in the middle of the map. Make sure to escort it with your Jans. From there ship Spahi and start massing cav archers. Yes you heard right, Cavalry Archers from your fort. Next send Mam and Stradiots. If you dont have enough resources for the mercs then build hussars. The cav+cav archer combo works perfectly against Sioux since their army usually consist of light infantry and cav. As an added bonus Cav archers also counter those annoying rifle riders. From there its just a matter of raiding,cutting him off resources and putting him under constant pressure.
A well placed fort works wonders against Sioux in early fort or colonial. Sioux will not have the eco he needs to mkae an army and have villys on Seige Dance. The sioux colonial army simply won't have enough siege unless they massed war clubs which reallly doesn't happen.
Questions, comments or criticism are all welcome.