unfortunately your post is not specific as to which rileys you might be looking for.
i would recommend dates, locations, children and spouse so that people can match records.
this is a common surname and there are 661 rileys on the dawes roll.
genealogists use names, dates, locations, children and spouses to match records. if you have a common surname, you need to give more information rather than less. if you post about women, it is helpful to include the maiden name and the married name and designate which one is the maiden name.
first of all, heritage and tribal enrollment are two different things. many times natives didn’t apply for enrollment because 1) they didn’t qualify, 2) they were philosophically opposed to enrollment, 3) they didn’t have documentation, or 4) they were mississippi choctaw and their ancestor had accepted land or benefits in lieu of tribal enrollment.
the dawes roll was taken 1896-1906, so you should trace your ancestors down to that time period. mostly, they had to be living in oklahoma by that time and agree to live there permanently.
if the name is common, you may find too many possible records.
the tribe has an excellent information to help you. it is found under genealogy advocacy.
http://choctawnation.com/services/departments/community-services/
mississippi choctaw and choctaw tribe explained here:
http://en.wikipedia.org/wiki/Choctaw_Trail_of_Tears
i have collected many resources over the years. if you want to write to me, shamlet76@gmail.com and request the choctaw resource list, i will be glad to send it to you.
i am just a volunteer that wants to empower people to learn how to do genealogy.
suzanne hamlet shatto