One oral tradition has the Rineys migrating from Ireland where their name was O’Raigne.

Another oral history on the Rineys as passed down by people living in the mountainous region of Gleninchaquin (eight miles, south west of Kenmare, IRELAND) and throughout the area strongly hint that we were originally O'Neills. Somehow related to the last great Irish leader the "Great O'Neill" as he was then known. Hugh O'Neill was the Earl of Tyrone who linked up with the Spanish in a vain attempt to wrest Ireland from English rule. They were defeated in 1601 at the Battle of Kinsale by Lord Mountjoy. After the debacle they fled and it is believed that some of our O'Neill ancestors managed to avoid capture by taking to the high grounds, the Caha Mountain range that lies between County Cork (the site of the Kinsale battle) and County Kerry. "Ri" is the Irish word for king, and "ney" is an abbreviated version of Neill. When put together we have "Riney" which means King Neill -- this is the oral history as passed down over all these years.

The Rineys probably first came to the United States sometime before 1750. (Supposedly as part of the Lord Baltimore colonies of Maryland.) Family tradition says that four Riney brothers came from Ireland and were among the first settlers of St. Mary's County, Maryland. Exact arrival date of the Rineys is unknown and documentation has not been found to confirm what has been handed down by word of mouth. Some settled in Maryland, but most went on to Kentucky. The Rineys were among the first settlers of Washington County, Kentucky, migrating from Maryland in the latter part of the 18th Century. Sixty families in the community of St. Mary's County, Maryland, had pledged themselves to migrate to the Kentucky countryside within a specified time.

The first migration was about 1785, and during the next years, the second group, with which the Riney family was associated, arrived at Pottinger's Creek neighborhood, near Holy Cross Church. This was the first Catholic church erected west of the Allegheny Mountains. These settlers traveled through the wilderness to Pittsburgh, then down the Ohio River on flatboats to the Falls of the Ohio (now Louisville), a place that at that time was merely a small settlement of less than a dozen cabins.

A number stayed in that state (plenty of descendants remain there to this day), or near there, in Missouri (where they helped to found city and cathedral of St. Patrick, Missouri, in Clark County) and Illinois, but some traveled on to Texas, Arkansas, etc. etc. There are many more Rineys today in the states than remain in Ireland.

In his will of 1818, Thomas Riney declared..."First I give my soul to the almighty. Second, I give and bequeath unto my beloved wife, Priscilla, all my estate, real and personal during her legal life and after her death or marriage, I give and bequeath unto my son , Robert Riney, One - third of the tract of land adjoining his on which I now live. Also, I give and bequeath unto my son Robert, my negro boy, Tom, during the life of my son Augustin (institutionalized) and after the death of my son Augustin, the said Tom is to belong to my daughter, Susannah Wheatly. Now, after the death of my wife, the residue of the estate is hers to distribute among her children as she pleases."
 
This seems to imply that Thomas's own children were named in the will while there were others belonging strictly to Priscilla by another marriage that may well have been to another Riney.