Transparent Gradient for Print

Some of the projects I work on involve printing an image with gradient transparency on glass.  The printer I am working with can print up to 1,200 DPI, and it can print a 100% transparent pixel or a 100% opaque pixel.  The only solution I can think of for this is to convert the image to a dithered pattern of solid and transparent pixels, but I can't figure out how to automate the process.

Using a grayscale image as the example, white would be transparent and black would be printed.  a 50% gray pixel should be dithered to print every other pixel (alternating black and clear), 75% black would print 3 out of 4 pixels, etc.  Is there a way to do this?  I tried converting to halftones, but can't keep the resolution high enough for the image quality.

How would you solve this issue?