I tried this solution but above command is giving error.
Any solution?

mysql -uroot -S /var/lib/mysql/mysql.sock -ppassword
mysql -uroot -S /var/lib/mysql2/mysql.sock -ppassword

or create script to easily connect with mysql cli
if your default mysql is inside “/usr/bin/” then create 2nd in the same directory as
touch /usr/bin/mysql2
chmod +x /usr/bin/mysql2

edit the file and paste given below lines and save it
vim /usr/bin/mysql2

#!/bin/bash
mysql –socket=/var/lib/mysql2/mysql.sock $1 $2 $3 $4 $5 $6 $7 $8

now on linux console simply type mysql2 and you will connect with your 2nd instance.

testmachine:/var/lib/mysql2 # mysql -h 127.0.0.1 -P 3307 -uroot -pvembu
ERROR 2003 (HY000): Can’t connect to MySQL server on ’127.0.0.1′ (111)

Now it generates new configs in /etc/mysql$I, new init.d script /etc/init.d/mysql$I and setups new DB.
You can start DB by ‘/etc/init.d/mysqlN start’ and stop it by ‘/etc/init.d/mysqlN stop’. Also possible to do ‘killall mysqlN’

Please don`t forget to set root password as script not does this.

Work was done for Debian 6.0.1.

#!/bin/bash

i=$1

if test -z “$1″ # No command-line arg supplied?
then
echo “Usage: `basename $0` instanseNum”
exit
fi

if test -d “/etc/mysql$1″ #
then
echo “Error: Directory /etc/mysql$i already exists!”
exit
fi

port=$(($i+3306))

#make new init script
cp /etc/init.d/mysql /etc/init.d/mysql$i
#make symlink for binary ( to make ‘kill’ working )
ln -s /usr/sbin/mysqld /usr/sbin/mysqld$i
#Fix init script
sed -i “s/\/etc\/mysql/\/etc\/mysql$i/g” /etc/init.d/mysql$i
sed -i “s/\/etc\/init.d\/mysql/\/etc\/init.d\/mysql$i/g” /etc/init.d/mysql$i
sed -i “s/\/usr\/bin\/mysqld_safe\ >/\/usr\/bin\/mysqld_safe\ –defaults-file=\/etc\/mysql$i\/my.cnf\ –mysqld=mysqld$i\ >/g” /etc/init.d/mysql$i
sed -i “s/\/usr\/sbin\/mysqld\ –print-defaults/\/usr\/sbin\/mysqld$i\ –defaults-file=\/etc\/mysql$i\/my.cnf\ –print-defaults/g” /etc/init.d/mysql$i
sed -ri “s/\ mysqld$/\ mysqld$i/g” /etc/init.d/mysql$i
sed -ri “s/\ mysqld;/\ mysqld$i;/g” /etc/init.d/mysql$i
sed -ri “s/\”mysqld\”/\”mysqld$i\”/g” /etc/init.d/mysql$i

#make new config files from existing one
mkdir /etc/mysql$i/
#cp -rt /etc/mysql$i/ /etc/mysql/
cp -R /etc/mysql/* “/etc/mysql$i”

#Fix paths in script
sed -i “s/\/etc\/mysql/\/etc\/mysql$i/” /etc/mysql$i/debian-start
sed -i “s/\/etc\/init.d\/mysql/\/etc\/init.d\/mysql$i/” /etc/mysql$i/debian-start

#And make new config debian.cnf
dc=/etc/mysql$i/debian.cnf;
pass=`perl -e ‘print map{(“a”..”z”,”A”..”Z”,0..9)[int(rand(62))]}(1..16)’`;
cat /dev/null > $dc
echo “# Automatically generated for Debian scripts. DO NOT TOUCH!” >>$dc
echo “[client]” >>$dc
echo “host = localhost” >>$dc
echo “user = debian-sys-maint” >>$dc
echo “password = $pass” >>$dc
echo “socket = /var/run/mysqld/mysqld$i.sock” >>$dc
echo “[mysql_upgrade]” >>$dc
echo “host = localhost” >>$dc
echo “user = debian-sys-maint” >>$dc
echo “password = $pass” >>$dc
echo “socket = /var/run/mysqld/mysqld$i.sock” >>$dc
echo “basedir = /usr” >>$dc

# If this dir chmod go+w then the admin did it. But this file should not.
chown 0:0 $dc
chmod 0600 $dc

#Fix paths and so on in my.cnf
sed -i “s/3306/$port/g” /etc/mysql$i/my.cnf
sed -i “s/mysqld.sock/mysqld$i.sock/g” /etc/mysql$i/my.cnf
sed -i “s/mysqld.pid/mysqld$i.pid/g” /etc/mysql$i/my.cnf
sed -i “s/\/var\/lib\/mysql/\/var\/lib\/mysql$i/g” /etc/mysql$i/my.cnf
sed -i “s/\/var\/log\/mysql/\/var\/log\/mysql$i/g” /etc/mysql$i/my.cnf
sed -i “s/\/etc\/mysql/\/etc\/mysql$i/g” /etc/mysql$i/my.cnf

#Make some dirs for logs and data
mkdir /var/log/mysql$i
chown -R mysql:adm /var/log/mysql$i
chmod 2750 /var/log/mysql$i

mkdir /var/lib/mysql$i
chown -R mysql /var/lib/mysql$i
chmod 700 /var/lib/mysql$i
touch /var/lib/mysql$i/debian-5.1.flag

#Create new database
mysql_install_db –user=mysql –datadir=/var/lib/mysql$i/

#UPdate debian-sys-maint user in new database
MYSQL_BOOTSTRAP=”/usr/sbin/mysqld –bootstrap –user=mysql –skip-grant-tables –datadir=/var/lib/mysql$i”

replace_query=`echo -e \
“USE mysql\n” \
“REPLACE INTO user SET ” \
” host=’localhost’, user=’debian-sys-maint’, password=password(‘$pass’), ” \
” Select_priv=’Y', Insert_priv=’Y', Update_priv=’Y', Delete_priv=’Y', ” \
” Create_priv=’Y', Drop_priv=’Y', Reload_priv=’Y', Shutdown_priv=’Y', ” \
” Process_priv=’Y', File_priv=’Y', Grant_priv=’Y', References_priv=’Y', ” \
” Index_priv=’Y', Alter_priv=’Y', Super_priv=’Y', Show_db_priv=’Y', “\
” Create_tmp_table_priv=’Y', Lock_tables_priv=’Y', Execute_priv=’Y', “\
” Repl_slave_priv=’Y', Repl_client_priv=’Y', Create_view_priv=’Y', “\
” Show_view_priv=’Y', Create_routine_priv=’Y', Alter_routine_priv=’Y', “\
” Create_user_priv=’Y', Event_priv=’Y', Trigger_priv=’Y’ “`;

echo “$replace_query” | $MYSQL_BOOTSTRAP
#2>&1 | $ERR_LOGGER

#Now U can start new db instance by ‘using /etc/init.d/mysql$i start’ and stop it in the same way.
#
# I was lazy enough to generate and set root password to new db. Do it yourself.
# mysqladmin -h 127.0.0.1 -P 3308 -u root password ‘the2NewSuper5234Passweord’
# mysql -h 127.0.0.1 -P 3308 -u root -p
# mysql -S /var/run/mysqld/mysqld2.sock -u root -p