Apple Script help - how do I tell OS X to not launch a specific app during a specific time period?
How about the following? It can be used as an app launcher. It doesn't stop the user of launching the app but for a child it should do. You could also easily convert it to a background script to continuously monitor for desired app and kill it once usage goes beyond allowed time block.

Hope it helped.

# The times to check. Use HH:MM:SS 24HR format or AM/PM
set sTime to "19:00:00" # 7PM
set eTime to "20:00:00" # 8PM

# Get just the date from shell; quicker
set tDate to getShortDate()

# Setup Date &amp; Time vars for start and end
set sDateTime to tDate &amp; " " &amp; (sTime)
set eDateTime to tDate &amp; " " &amp; (eTime)

# Convert dates to Epoch
set sEpoch to toEpoch(sDateTime)
set eEpoch to toEpoch(eDateTime)

set epochNow to getEpoch()

if epochNow &gt; sEpoch and epochNow &lt; eEpoch then
    tell application "Finder" to set tProcesses to name of processes
    if (tProcesses contains "Firefox") then
        display dialog "Firefox is currently banned"
        #Kill Firefox app
    end if
else
    #log "Launching Firefox..."
    activate application "Firefox"
end if

on getEpoch()
    return do shell script "date \"+%s\""
end getEpoch

on toEpoch(aDateTime)
    return do shell script "date -j -f '%Y-%m-%d %T' '" &amp; aDateTime &amp; "' +'%s'"
end toEpoch

on getShortDate()
    return do shell script "date \"+%Y-%m-%d\""
end getShortDate