Here is a list of libraries that may offer non-residents a library card.
Before you send money/credit card info, email first to make sure they will still issue you one and if it includes Overdrive privileges.
Other libraries on the list may be a better fit. Fewer residents utilizing service with a good selection available. While Brooklyn has over 31,000 titles they may not have what you wish to read and a population of 2.5 million. Philly has 12,000 titles with 1.5 million people. Monroe County NY has 9500 titles with 750,000 people.