In principle all polymers which contain phenolic groups, thioethers or thiols are polymeric antioxidants. Poly-L-tyrosine contains phenolic groups and must therefore be an antioxidants as well as poly-L-methionine, which contains thioethers. Tannic acid contains many gallic acid ester and is therefore a strong antioxidant and cheap. Polyphenylene sulfide is also an antioxidant but it is insoluble in common solvents. Perhaps it is sufficient to make by grinding a sub micron powder which can be used. To make polyphenylene sulfide water soluble it can be sulfonated (many procedures exist for this purpose). You can also make water soluble polysulfides by yourself with thiol ene click chemistry of diallylethers of polyethylene glycol with dimercaptanes.