I have a screen shot I take in my mobile app. The screen shot takes about 32 KB when saved as a png on a disk.
I am sending these to a central SQL Server and 32 KB
If monochrome image is acceptable, you can try TIFF G4 (lossless compression). TIFF G4 is known for being very effective in file size to store black and white image. Unfortunately I dont have any info available on how it compares to PNG, but worth investigating into it.
Here is the info and example on how to do it in C#