Dale: You may already have the following but since I've been researching my own Irish ancestors in the Irish Hill section of Indianapolis, Marion County (Donahue, Sullivan, Shea, White, Leary, McKee and more, research which has expanded to include other families which ended up in Holy Cross Parish), I've become something of a collector of Irish names. Although I suspect the following is your Riley group, please remember to verify that this does indeed pertain to your family.

1870 City Directory
Riley Michael, lab, resides 286 S Tennessee
Riley Timothy, Lab. resides 287 S Tennessee

1880 Census, Indianapolis, Marion County, Indiana
Pg. 503A, Enumeration Dist 122, 6/7/1880, Charles B. Burger
S Tennessee Street
Hse # 287, Dwg # 163, Fam # 255
Riley Timothy, w, m, 67, married, Common Laborer (illness on day of visit: consumption), b Ireland, both parents b Ireland
Riley Elizabeth, w, f, 52, wife, married, Keeping house, b Ireland, both parents b Ireland
Riley, Timothy, w, m, 22, son, single, Common Laborer, (checkmark under "cannot write"), b Indiana, both parents b Ireland
Riley Michael, w, m, 17, son, single, works in Pork House, b Indiana, both parents b Ireland
Riley Matthias, w, m, 13, son, single, no occupation, b Indiana, both parents b Ireland
Riley Johnny, w, m, 12, son, single, attending school,, b Indiana, both parents b Ireland
Riley Mary E., w, f, 6, daughter, single, attending school, b Indiana, both parents b Ireland
Approximate year of birth in following record matches your Michael's brother Timothy:
Marion County Indiana Birth Records, July 1882 to Sept 1907
O Riley Joseph, 14th child born, m, w, 1905 Feb 24, 1664 Harvey, alive, legitimate, mother Mary Hiles, 40, same address, b Amelia OH; father Timothy M. O'Riley, 46, fireman, b Indpls., reported by Dr. Hiles (same name as
mother), no address, 1905 Feb 27
Regards, Dianne (diannero@msn.com)