It's possible to define a subset of the deflate bitstream that only does simple RLE compression, and I've done so: https://gist.github.com/DavidBuchanan314/b223bce114ec715a66f...
But, for logo/icon sized bitmaps, you can generally get away without needing compression at all. A 128x128 1bpc image is a mere 2KB.
[1] discussed here https://news.ycombinator.com/item?id=38515571