Sometimes sellers who have been unable to sell their property will consider rentals. You can try to contact the listing agents of some of the properties for sale to see if any are considering renting. Cross which is for rent, came on the market as a rental, but had been for sale (still is) - for several months prior to being offered as a rental.
If you will consider Red Bank or Oceanport, you might find a few more options opening up. However, I did note that you said, "specifically Little Silver." It's a small town and there have been 11 rentals YTD, which is a 1.375 average per month. Based upon that, it's not likely that many options will open up. Maybe a great match for you will hit the market. However, you might want to have a Plan B, just in case.
Try looking on CraigsList, for rentals also.
I do not know of any potential rentals in Little Silver other than the two you referenced.
Deborah "Deb" Madey