Try something like this:
If you are happy with terminal, just create a new file and put in something like this:
#!/bin/sh
sudo java -jar littleSniffer.jar
and save the file as blah.command (the .command extension runs the sh file in terminal on double click).
If you would like something a bit nicer, you could use the osascript command like this:
#!/bin/sh
osascript -e "do shell script \"java -jar littleSniffer.jar\" with administrator privileges"
Which will use a GUI request for the root password.
NOTE: If your .command file isn't running, you may need to:
chmod +x blah.command
to make it runnable.