Welcome to the JavaRanch, Gigi!
OS package managers rarely give you a choice of what version of a product to install. At best, occasionally you'll get 2 major versions to chose from, such as Tomcat 7 and Tomcat 8.
That's because most packages are less forgiving of minor version variances than
Java systems are and because the distro managers don't want to waste a lot of effort on similar-but-not-identical software.
The way to deal with that normally would be to download the Tomcat ZIP file straight from tomcat.apache.org and simply unzip it, but you're indicating a problem with an init script, which wouldn't be part of that download.
At best, you might be able to browse back generations of the Debian package sources in their archives (presumably git archives) and build one yourself.
Of course, Tomcat 6 releases before about 6.0.28 had some significant exploits in them, so no production system should be running them. For that matter, no actively-maintained system should still be running Tomcat 6 anyway - we're moving towards Tomcat 9 at the moment.