If you want latest version,which is not available on ubuntu repos, there are following alternate ways of getting it.
Now as you don't want to install manually,lets speak about other methods.
once you find the repository you need,open a terminal and type.
sudo add-apt-repository ppa:(Your ppa here)
sudo apt-get update
sudo apt-get install tomcat
you will first have to temporarily block the repo which contains older version of tomcat,or they will interfere.you can do this by
sudo add-apt-repository -r ppa:(Your ppa here)
and dont forget to add it back, once you are done.
this link provides the source code.for building and installing software read software documentation/forums and compile easy how to
download package using website or any other place.then use alien
to convert package.read alien man pages
for help on using alien.