Legally, no. Here's the deal:
If a complex / community posts a "No Tresspassing" sign, it really means nothing. It's just there to scare people away. If an individual home within that community posts a "No Tresspassing" sign on their own home, JWs should not knock on that door.
If a complex / community posts a "No Soliciting" sign, it means nothing for JWs since they are not soliciting (normally... I'll get to that in a minute). Same goes with an individual home. From a legal perspective, "no soliciting" does not apply to preaching religion.
However, when JWs have campaigns where they are going around canvasing, they may very well fall into the "soliciting" category. Just going around and leaving those invitations / tracts is NOT preaching, and there could be a good case in court to make that activity fall under local canvasing / soliciting ordinances. This has not, to my knowledge, ever been challenged. And, this has not been specifically addressed by WTBTS. The last letter regarding all this came out to the BOEs prior to all the campaigns JWs have been having.
Back to your situation: If someone in your community tells JWs to not be there, they will go away until another time. If you manager tells JWs to not be there, JWs are supposed to get their information, (name, community name, address), give it to the Service Overseer. The Service Overseer / Secretary is supposed to write a letter to the Legal Dept. The Legal Dept. will come back with a letter telling them not to work that community for a period of one year. (I guess is that they home the manager changes or forgets what they told them to begin with.)
Another thing you can do is have your manager write a letter to the local KH or even to the branch requesting that they not have JWs visit the community.
The problem in a community is that you personally cannot speak for everyone in your community. But, your manager DOES have the power to ask them to leave and not come back, and the JWs are supposed to follow protocol. It's important that your manager identifies him/herself as the manager, not just a homeowner.
Another thing that might work is putting up a sign that says: "No Soliciting. No Tresspassing. That includes religious groups." This may very well dissuade JWs from entering the complex / community.