Is it possible to allow usage for an app or program for a specific times on a Mac? I was trying to achieve this using a second account (which is the admin account) and Parental Controls, but it seemed this isn't possible to do so.

I know there are some programs which you can download that help you with this, (Cold Turkey, for example). But, it would be much easier if I could do this using only tools already available on macOS.
You can do this with two built in tools:


Gatekeeper to allow/disallow access to apps (I've written about it in this post)
Launchd to handle the schedule


Gatekeeper

Using Gatekeeper, we can create "rules" that allow you to block/enable apps.  Using your example, we can create a list of Apps that is only allowed to run on Fridays:

spctl --add --label "FridayApps" /Applications/SomeApp.app 


The benefit of this, is that you can add multiple apps with the same label and enable/disable them in one single command:

sudo spctl --disable --label "FridayApps"   &lt;---- For Saturday thru Thursday
sudo spctl --enable --label "FridayApps"    &lt;---- For Friday


Launchd

For this you will need  a simple script to enable/disable the apps and you need to run this as a daemon (needs sudo privilege) so it has to reside in /Library/LaunchDaemons.  

I used the naming convention com.user.FridayApps.plist and FridayApp.sh for the script.

Bash Script:

#!/bin/bash

DOW=$(date +%u)   # Sets the Day of Week; 5 = Friday
TOD=$(date +%T)   # Sets the time of Day
start="12:00:00"  # Sets start time   
end="23:59:00"    # Sets end time

if [ $DOW -eq 5 ]
then
    if [[ "$TOD" &gt; "${start}"  &amp;&amp;  "$TOD" &lt; "${end}" ]]
    then
      /usr/sbin/spctl --enable --label "FridayApps"
    fi
else
    /usr/sbin/spctl --disable --label "FridayApps"
fi


Launchd .plist

&lt;?xml version="1.0" encoding="UTF-8"?&gt;
&lt;!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd"&gt;
&lt;plist version="1.0"&gt;
&lt;dict&gt;
    &lt;key&gt;Label&lt;/key&gt;
    &lt;string&gt;com.user.FridayApps&lt;/string&gt;
    &lt;key&gt;ProgramArguments&lt;/key&gt;
    &lt;array&gt;
        &lt;string&gt;/User/MyName/script/location/FridayApps.sh&lt;/string&gt;

    &lt;/array&gt;
    &lt;key&gt;StartCalendarInterval&lt;/key&gt;
    &lt;!--  Weekdays are 1 - 5; Sunday is 0 and 7   --&gt;
    &lt;array&gt;
        &lt;dict&gt;
            &lt;key&gt;Weekday&lt;/key&gt;
            &lt;integer&gt;5&lt;/integer&gt;
            &lt;key&gt;Hour&lt;/key&gt;
            &lt;integer&gt;12&lt;/integer&gt;
            &lt;key&gt;Minute&lt;/key&gt;
            &lt;integer&gt;01&lt;/integer&gt;
        &lt;/dict&gt;

        &lt;dict&gt;
            &lt;key&gt;Weekday&lt;/key&gt;
            &lt;integer&gt;6&lt;/integer&gt;
            &lt;key&gt;Hour&lt;/key&gt;
            &lt;integer&gt;00&lt;/integer&gt;
            &lt;key&gt;Minute&lt;/key&gt;
            &lt;integer&gt;00&lt;/integer&gt;
        &lt;/dict&gt;
    &lt;/array&gt;

&lt;/dict&gt;
&lt;key&gt;RunAtLoad&lt;/key&gt; 
&lt;true/&gt;
&lt;/plist&gt;

##Load the `.plist`

sudo launchctl load com.user.FridayApps.plist


How this works

What's happening here is two things:


launchd is running a script twice.  Once at the time to run it on and another time to turn it off 
a simple bash script to turn on/off the enabled app.  It verfies the date and then runs the appropriate command