Great question.  There are no published recommendations for canning persimmons.  Persimmons in the borderline acid category (pH 4.2-4.7), so it would not be safe to water bath can unless there were recommendations for acidification.  There are also no recommended procedures for pressure canning.  Therefore, we cannot recommend procedures for either of these preservation methods.

Freezing and drying are recommended methods for preserving persimmons.  See references below for recommendations on how to prepare persimmons:

Freezing:

https://nchfp.uga.edu/how/freeze/persimmon.html

Drying:

https://nchfp.uga.edu/publications/uga/uga_dry_fruit.pdf

Sorry to not be of more help. Best of luck!