Check if ColdFusion server is running or not

you can use a third party tool like server monitoring software
http://www.dnsstuff.com/free-server-monitoring-tools
http://www.monitis.com/blog/11-top-server-management-monitoring-software/

OR

if you have a third server you can have it ping the CF server x minutes looking for a response

set up a cf page on each of the servers you want to monitor
cfnineserver.com/mymonitor.cfm all the page does is
<cfsetting
enableCFoutputOnly = 'yes'>
<cfoutput>1</cfoutput>

then form the third server use cfhttp or php curl to accesss the monitor page, and if any value other than http 200 value 1 is returned send an email or text message to the team

I have only one server for the application also cant use any 3rd party tool. Can we put mymonitor.cfm in same server in some way ?

not really, it won't run if the cf goes down, so you would need a negative condition process, your team would constantly get pings while the service is up and nothing if it goes down, problem with that is people stop caring, after a few pings, they start to ignore it.

Why no third-party software?

you have two versions of cf, 9 and 5, can you get them to ping each other?

what if you set up an AWS as your third party server?
https://aws.amazon.com/s/dm/optimization/server-side-test/free-tier/free_np/#details
and ran it form there, just has to ping your server every few minutes?