According to Senate historians, there are no formal records. One such historian claimed that since the rules inception in 1902, he is aware of two such instances. The last time dating back to the fifties. However, there is evidence of it happening much later.
An important issue can be seen in that second article. Some things can be stricken from the official record. So between not officially recording instances of rule XIX, and the ability to alter the record, we cannot know for certain how many times it has been used, or how many times it may have been threatened but not used because the senator followed the rules once warned.