I am not aware of being able to not open a file and append to it, if you are using JMP tables. Here is as close as I think you can get using JMP tables.
names default to here(1);
new table("New Data",new column("name", character,set values({"BILLY","JIMMIE"})));
dt = open("$DOCUMENTS\Discussion Group\my.csv",private);
dt<< Concatenate(Data Table ("New data") , append to first table);
dt << Save("$DOCUMENTS\Discussion Group\my.csv", Replace(1));
close( dt, nosave );
However, if you write the JSL to convert your data table "New Table" into a character string, which is a comma separated values character string, you can us
Save Text File(path, character string, mode("append");
and it will append to your .csv file without having to open it
Jim