You can request a bike rack by calling 311, but the most effective route is to work with your local community board to develop a comprehensive on-street bike parking plan for the whole neighborhood, enabling the DOT to install dozens of racks at once. Contact bike[at]transalt[org] for tips on engaging your community board to tackle this problem.
A guide to the dos and don'ts of on street bike parking is available on the Biking Rules website: bikingrules.org/biking/parking
To learn more about the need for more on-street bike racks, see T.A.'s report: Improving Outdoor Bike Parking and Policy in New York City (PDF)