Carbon... Activated Carbon. Charcoal is what you put in your grill

(common, contagious mistake)
In order for Activated Carbon to work, water or air need to be flowing through it. The carbon attracts specific elements of tiny particle sizes.
On large particles such as Algae, carbon does nothing, as millions of fish tank keepers can attest to :/
Algae thrives in certain conditions, PH range, sun, and organic matter in the water to supply nitrogen. Every time birds come to drink, they leave debris from their beaks (food, grooming dander, soil) even unintentionally. My birds do it on purpose, coming to dump dirt out of their mouths when they've been rooting around for bugs.
So the single best way to slow the growth of Algae is to keep dumping the debris before it has a chance to decompose. You can only slow it down.
In a cleaner system, such as nipples, the container/ supply lines should be black to eliminate any trace of light getting through.
If that's not possible, PH is next. It's very hard to manipulate the PH of water and have it stay stable, more work than cleaning out waterers anyway. If your water is already near the low end of the spectrum, pond keepers often have success throwing in whole bales of barley straw.
In hard well water like we have there's no point... acidifying agents are neutralized by the minerals (calcium especially).