Man,
I don't know of any other. I think there used to be one somewhere in Firestone, Harbel, or the Buchanan area but I am not sure ... haven't been there, anyway. On this same issue, I did not know of those others besides the ATS and SKD both of which are in Monrovia and it's suburbs respectively.
I believe the premier league and other cup mathes are played at the ATS. The LFA proposed that all other teams have their own playing field(s) since there would be both home and away games in competitions. However, many of our fields are sub-standard. Yet, the LFA approves them for playing reasons. For instance, the former Barcelona used Barnersville Estate field as their playing pitch. It is a very small playing field.
When I played for Exodus (a youth team on Barnersville Oldfield), we played on a little hilly area in a neighbor's backyard. By the way, my team changed its name just before entering the LFA 3rd Division league in 1999.