The Troy-Miami County Public Library (Main Branch) has the Troy Daily News from 1950 to the Present. 

Laura Girolamo is reference librarian and would be able to assist you in that area. lgirolamo@tmcpl.org

 
The Local History Library (local history branch of the TMCPL) has early newspapers 1820's (Troy) - 1952 (about 1864 - 1952 is the Miami Union, a county paper published in Troy).
 
As far as the Local History Library, if you have the exact date or close (1 - 2) weeks, we could get you the obit photocopied or faxed for about $2.  If you need us to make a search of other records to locate the date, then we request $5/hour, plus copies (.10/copy), and postage (one or two obits will not exceed .37).