I've received a lot of contradictory e-mails from folks discussing the name of the Disney TV series on which the Texas John Slaughter episodes aired. All the folks who told me it was The Wonderful World of Disney or Disney's Wonderful World of Color or any other such permutation were wrong. I was also wrong when I said it was Disneyland, though I have a great excuse: The back of that Texas John Slaughter still I featured in this post said it was from the TV series, Disneyland.
The definitive answer comes from my old chum, Bill Cotter, who authored the (emphasis on "the") book on the subject, The Wonderful World of Disney Television. Bill's book is now out of print but that link will take you to an Amazon page via which you can usually snag a used copy for a reasonable price…and if you're interested in the subject, you should. Bill writes me to say…
10/31/058 was the debut of the show, and it was on Walt Disney Presents. This was the name of the anthology series between the two previously mentioned titles [Disneyland and The Wonderful World of Color], and it was used for three seasons (1958-1959, 1959-1960 and 1960-1961). After that it was on to color, and no more Texas John Slaughters, sad to say. That arc was one of my favorites of the time.
Bill also directs me (and therefore, you) to this page on his website which lists what was on those shows and when. This should settle matters.