Most Overdrive libraries support searching for books to recommend, but a few don't, most notably the Orange County Library System (which allows you to acquire a non-resident library card without visiting in person). But, just because you can't search for books to recommend, that does not mean you cannot recommend books.
Simply search for the book at any Overdrive library that allows recommendations, find the book you want, and click on the link to get to the main book page. It will look something like this:
Code:
https://brooklyn.overdrive.com/media/3033933
Then, copy the number at the end of the URL:
Go to the library that doesn't support searching for recommendations, and pull up any book page. Paste the number you copied in place of the number in the URL, and you will get the book page with an enabled "Recommend" button.
The advantage to this is that even if the library doesn't want recommendations because they don't pay attention to them, it enables you to get on the hold list early if the library does buy the book. Otherwise, you have to keep checking the library to see if they have bought the book or not, and then jump into the hold list.
EDIT: I found this does not work if the book has no formats listed. In that case, you get a greyed out "Unavailable" button.