There is a free service available to you called Listing Book. It is fed off of the Multiple Listing Service.
Once you enter your requirements, this service will show you everything that is available to you. When new listings come on that match your requirements, you will be automatically notified.
If this rental exists but is over your desired price point, when it drops in price into your range, you will automatically be notified.
All that is required to set you up is your first name, last name & email address. You will be sent a link and your own password.
This service does not cost you anything and does not lock you into using me as your Realtor; we still have free choice.
If you are interested, my email is email@example.com or 631-425-6150.