Here are the examples I've found so far:
1. Captain Marvel and His Country Cousin. This story was published in Captain Marvel Adventures #26 (published June 30, 1943). Willard Batson from Arkansas tracks down Billy Batson and introduces himself as Billy's cousin! However, Billy finds out that there is no relationship at all.
2. Captain Marvel and the Last of the Batsons! This adventure comes to us from Captain Marvel Adventures #51 (published November 28, 1945). Billy meets 'Wild Bill' Batson who claims to be the last of the Batsons from out West and Billy is his long-lost grandson! But by the end of the story, Captain Marvel discovers Wild Bill's true long-lost grandson. Once again, Billy meets a Batson that is not a blood relative!
These are the only examples I've found so far. As I discover more, I'll update this article!