A simple modification to https://github.com/heroku/heroku-buildpack-java to download and include Tomcat 7 in a your build directory at /tomcat. You can then use the Maven AntRun plugin to overwrite any files configuration files and launch the project as necessary. See https://gist.github.com/4575349 or below for an example build configuration.
<build>
<plugins>
<!-- copy configurations for Heroku Tomcat -->
<plugin>
<artifactId>maven-antrun-plugin</artifactId>
<executions>
<execution>
<id>copy-conf</id>
<phase>install</phase>
<configuration>
<tasks>
<copy todir="${project.build.directory}/../tomcat/conf">
<fileset dir="deploy/conf" />
</copy>
</tasks>
</configuration>
<goals>
<goal>run</goal>
</goals>
</execution>
<execution>
<id>copy-project</id>
<phase>install</phase>
<configuration>
<tasks>
<copy todir="${project.build.directory}/../tomcat/webapps/ROOT">
<fileset dir="target/${project.build.finalName}" />
</copy>
</tasks>
</configuration>
<goals>
<goal>run</goal>
</goals>
</execution>
</executions>
</plugin>
</plugins>
</build>