You can use a date literal in JSL or the formula editor. You just need to use the ddMONyyyy format.
date=22Jul2020;
tomorrow=22Jul2020+in days(1);
show(date, tomorrow, format(tomorrow, "mm/dd/yyyy"));
in the log you get:
date = 22Jul2020;
tomorrow = 3678307200;
Format(tomorrow, "mm/dd/yyyy") = "07/23/2020";
Read more: Using dates, times, datetimes and durations in JMP
-Jeff