Where to begin? View online (very faded) death certificate for J. R. Connally (25 Dec 1882 - 23 Jun 1955) at http://pilot.familysearch.org/recordsearch/start.html#start
Per document, he was born in Newport, Jackson, AR and died in Abilene per informant, Mrs. J. R. Connally. Father identified as James Connally of Georgia? Familysearch.org pedigree by Laura Marie Mouton Conley (Elk Grove, CA) identifies parents as James Monroe Connally and Mollie McHenry. Find James R. Connally in 1930 TX-Abilene-District 5-Image 10. He's misidentified as James K., but that was the right person. The family consisted of: Margaret E.(44), James R.(18), Christene(15), Leonard H.(13), Chester W.(10), Wylie H.(7), and Wilma E.(7). Use Texas' Birth Index to research descendants. Chester Willard Connally and Mildred Gertrude Farmer have five births registered in Midland. Hubert Leonard Connally and Nell Dabney have two births listed in Taylor. James Richard Connally, Jr. and Norma Cornelia Kott have two births registered in Gillespie. Delma Christeen Connally and Roland Edward Gold have two children listed in Gillespie. Lots of kinfolks and that only scratches the surface. After digesting that, search for James Monroe Connally at family search.org in Arkansas. He was born about 1837 in Jackson, AL and died in Oil Trough, Independence, AR. He had five wives, so there were other siblings/halves? Lot's of ways to "corrupt" Connally so be prepared during your search.