You can get an 8-bit PNG with a small size, but you can often get as good of a quality with a JPG image.
For 8-bit PNG, add quantize=adaptive to the URL to get the smaller size.
PNG images support either 8-bit or 24-bit color, but can often be made much smaller without much visual degradation by application of color quantization. PNG files use fewer bits per pixel for palletized images.
Here is an example URL: