1つ目のTomcatをポート8009(デフォルト)、2つ目のTomcatをポート8010で起動します。
インスタンスは別々に起動・終了できるようにPIDファイルを出力するようにします。
RHEL6系です。

Tomcatのインストール

# wget http://ftp.yz.yamagata-u.ac.jp/pub/network/apache/tomcat/tomcat-6/v6.0.39/bin/apache-tomcat-6.0.39.tar.gz
# tar zxvf apache-tomcat-6.0.39.tar.gz

1つ目

# mv apache-tomcat-6.0.39/ /usr/local/tomcat

2つ目

# mv apache-tomcat-6.0.39/ /usr/local/tomcat_8010

Tomcatが起動時にPIDファイルを出力するようにする

1つ目

/usr/local/tomcat/bin/catalina.sh

if [ -z "$LOGGING_MANAGER" ]; then
  LOGGING_MANAGER="-Djava.util.logging.manager=org.apache.juli.ClassLoaderLogManager"
fi

# 追加 ここから ------------
if [ -z "$CATALINA_PID" ]; then
  CATALINA_PID=/var/run/tomcat.pid
fi
# 追加 ここまで ------------

# ----- Execute The Requested Command -----------------------------------------

2つ目

/usr/local/tomcat_8010/bin/catalina.sh

if [ -z "$LOGGING_MANAGER" ]; then
  LOGGING_MANAGER="-Djava.util.logging.manager=org.apache.juli.ClassLoaderLogManager"
fi

# 追加 ここから ------------
if [ -z "$CATALINA_PID" ]; then
  CATALINA_PID=/var/run/tomcat_8010.pid
fi
# 追加 ここまで ------------

# ----- Execute The Requested Command -----------------------------------------

ポートの変更(2つ目)

/usr/local/tomcat_8010/conf/server.xml

22c22
< <Server port="8005" shutdown="SHUTDOWN">
---
> <Server port="8006" shutdown="SHUTDOWN">
#ポート8080をコメントアウト
68a69
>     <!--
71a73
>     -->
90c92
<     <Connector port="8009" protocol="AJP/1.3" redirectPort="8443" />
---
>     <Connector port="8010" protocol="AJP/1.3" redirectPort="8443" />

起動スクリプト

1つ目

/etc/rc.d/init.d/tomcat

#!/bin/bash
#
# Startup script for the tomcat
#
# chkconfig: 345 80 15
# description: Tomcat is a Servlet+JSP Engine.

# Source function library.
. /etc/rc.d/init.d/functions

export JAVA_HOME=/usr/java/default
export PATH=$PATH:$JAVA_HOME/bin
export CLASSPATH=.:$JAVA_HOME/jre/lib:$JAVA_HOME/lib:$JAVA_HOME/lib/tools.jar
export TOMCAT_HOME=/usr/local/tomcat
export CATALINA_HOME=/usr/local/tomcat
export CLASSPATH=$CLASSPATH:$CATALINA_HOME/common/lib

CATALINA_PID=/var/run/tomcat.pid

start(){
    if [ ! `pgrep -F $CATALINA_PID 2> /dev/null` ]; then
        echo "Starting tomcat"
        /usr/local/tomcat/bin/startup.sh
        touch /var/lock/subsys/tomcat
    else
        echo "tomcat allready running"
    fi
}

stop(){
    if [ `pgrep -F $CATALINA_PID 2> /dev/null` ]; then
        echo "Shutting down tomcat"
        /usr/local/tomcat/bin/shutdown.sh
        rm -f /var/run/tomcat.pid
        rm -f /var/lock/subsys/tomcat
    else
        echo "tomcat not running"
    fi
}

case "$1" in
    start)
        start
        ;;
    stop)
        stop
        ;;
    restart)
        stop
        start
        ;;
    status)
        /usr/local/tomcat/bin/catalina.sh version
        ;;
    *)
        echo "Usage: $0 {start|stop|restart|status}"
esac

exit 0

2つ目

/etc/rc.d/init.d/tomcat_8010

#!/bin/bash
#
# Startup script for the tomcat
#
# chkconfig: 345 80 15
# description: Tomcat is a Servlet+JSP Engine.

# Source function library.
. /etc/rc.d/init.d/functions

export JAVA_HOME=/usr/java/default
export PATH=$PATH:$JAVA_HOME/bin
export CLASSPATH=.:$JAVA_HOME/jre/lib:$JAVA_HOME/lib:$JAVA_HOME/lib/tools.jar
export TOMCAT_HOME=/usr/local/tomcat_8010
export CATALINA_HOME=/usr/local/tomcat_8010
export CLASSPATH=$CLASSPATH:$CATALINA_HOME/common/lib

CATALINA_PID=/var/run/tomcat_8010.pid

start(){
    if [ ! `pgrep -F $CATALINA_PID 2> /dev/null` ]; then
        echo "Starting tomcat_8010"
        /usr/local/tomcat_8010/bin/startup.sh
        touch /var/lock/subsys/tomcat_8010
    else
        echo "tomcat_8010 allready running"
    fi
}

stop(){
    if [ `pgrep -F $CATALINA_PID 2> /dev/null` ]; then
        echo "Shutting down tomcat_8010"
        /usr/local/tomcat_8010/bin/shutdown.sh
        rm -f /var/run/tomcat_8010.pid
        rm -f /var/lock/subsys/tomcat_8010
    else
        echo "tomcat_8010 not running"
    fi
}

case "$1" in
    start)
        start
        ;;
    stop)
        stop
        ;;
    restart)
        stop
        start
        ;;
    status)
        /usr/local/tomcat_8010/bin/catalina.sh version
        ;;
    *)
        echo "Usage: $0 {start|stop|restart|status}"
esac

exit 0

Tomcat起動

1つ目

# chmod +x /etc/rc.d/init.d/tomcat
# /etc/rc.d/init.d/tomcat start

2つ目

# chmod +x /etc/rc.d/init.d/tomcat_8010
# /etc/rc.d/init.d/tomcat_8010 start

Tomcat 自動起動

1つ目

# chkconfig --add tomcat
# chkconfig tomcat on
# chkconfig --list tomcat
tomcat     0:off   1:off   2:on    3:on    4:on    5:on    6:off

2つ目

# chkconfig --add tomcat_8010
# chkconfig tomcat_8010 on
# chkconfig --list tomcat_8010
tomcat_8010     0:off   1:off   2:on    3:on    4:on    5:on    6:off