If you have any of the Steam version of CoH, you could technically use that to track your hours played. It wouldn't be accurate now if you're only about to this and if you already have play time recorded from back on live.
You'll have to redownload/reinstall the old files though (via Steam, of course), after that, right click on 'City of Heroes' from your library list. Click 'Properties' from the pull down menu and from the General tab below, for the Launch Options, type:
"C:\Homecoming\bin\win64\launcher.exe" %command%
win32 if you're using 32-bit to run the game and the target location of launcher.exe should be where you've installed it if anywhere else. Finally, run it like a regular Steam game.
Now I don't know if this is allowed though 😅