I wasn't familiar with Birm ...
Published by Kenneth Keil, P.E.
I wasn't familiar with Birm so I did a search. Go to https://www.cleanwaterstore.com/resource/frequently-asked-questions/about-birm-iron-filters/.
Based on the information at this site, it appears Birm is not the best selection for removing the manganese. However, your issue is algae. Have you measured the phosphorous concentration? Is your product tank and/or filters exposed to sunlight? After running the water through the Birm, what is the dissolved oxygen concentration? If it is near 0 and the detention in the product tank is long w/ exposure to sunlight and there is significant phosphorous, algae will be produced. If the filters/product tank are not covered, can you cover them? If the dissolved oxygen is near 0, I would suggest aerating the water to at least 1 ppm.
As some of the others have said, ozonation and chlorination would work. However, if the tanks are exposed to sunlight, I wouldn't coat the walls a dark color. Having personal experience with dark colored hypalon liners in wastewater lagoons, the liners heated the water in March in cold Colorado and algae formed. Coating the walls a dark color w/ exposure to sunlight would only aggravate the algae problem.