I have configured start-elk.sh and stop-elk.sh script in /usr/local/bin/
You should manage your daemon processes with SysV init scripts, systemd unit files, or whatever your distribution prescribes.
Kindly provide some scripts or please give some hints for where to create another instance of logstash..
You can run any number of Logstash processes, but depending on how you start it there are different pitfalls. If you want to continue using your *-elk.sh shell scripts (which I strongly discourage you from doing) you probably just need to make sure that logs are written to instance-unique locations and that state files like sincedb are stored in different locations. Without details it's not useful to get into specifics.