There's been much discussion about these photos. I bought my copies some 25 years ago from a fan club based outside Shreveport and they were sold as being from the Louisiana Hayride.
The problem is that the Jordanaires are in the photo. The first indication that they played on stage with Elvis comes from the review of the show in Memphis on May 15, 1956.
Elvis played his last ordinary Hayride show on March 31, 1956. His very last Hayride show was on December 15, 1956 but they are definitely not from that day.
The shirt Elvis wears we see for the first time when he leaves Dayton, Oh. on May 28, 1956 flying hom to Memphis. Elvis also wears the same jacket. The Jordanaires who played with Elvis the previous day wear, if not the same, then at least similar ties and jackets.
So my guess would be no earlier than the middle of May 1956 and no later than October 1956.
(1970 section updated August 16)