What about a suspension of a solid dye? If the grains are small enough, they'll stay for very long in suspension.
A solid dye can be mineral and less sensitive to chlorine than an organic dye. I'd try with carbon black, in the form of Indian ink, a few drops added to your solution. Or try other ones if you find grain sizes small enough, especially metal oxides, which are chemically inert and available as fine powder for paint artists.
I've no idea if the suspension will catalyse some decomposition or evolution of your solution.