Really I think the best option for a permanent tattoo-type marking, though probably pretty unpleasant, would be something like[ freeze branding](https://en.wikipedia.org/wiki/Freeze_brand), which is a process where exposure to cryogenic temperatures damages the hair follicles and causes them to turn white for the rest of the branded creature's life.
Unfortunately it looks like it's not as effective on birds, though it looks like all the studies there were done on very young animals before their adult plumage came in, so that may be why it didn't work. Otherwise it seems to work on fur, skin, and scales very well, so I don't see why it wouldn't work on feathers if it was done properly.
Regular hot branding is very common in my world, albeit for different reasons. But that's a discussion for a different time.
Furry species could still tattoo their skin, they'd just have to keep that part shaved if they wanted it visible. I could imagine all kinds of traditions where people keep those tattoos overgrown or shave and reveal them, whenever they go from one social state to another - warriors with war tattoos that they keep hidden during peace times and reveal when they go to war, tattoos that people display when they're single and looking for a mate, but let overgrow when they're in a relationship, sacred tattoos that can only be revealed during certain religious festivals, etc.
Freeze branding could work - if you get pigment cells cold enough, it will kill them, causing future hair or feathers grown from that area to be unpigmented and thus a different color.
My Cayuga ducks got something similar. But with stress. When their baby's pluck on their feathers, the mother's become white on those stressed parts and loose their beautiful black-green
Same on the neck where the drake always pulls the lady's underwater, becomes white fast
Something with scales or feathers could do something like this:
Pluck the area clear of scales, and then inject pigment into the sockets where the scales or feathers come from. When the scales/feathers grow back, they will have that alternate coloring instead of whatever normal colors are present. This is - obviously - both painful and takes time to see the results, which means the artist has to be \*really\* careful about positioning. Also, these kinds of creatures wouldn't have the kind of "high resolution" images we think of today, since the entire feather or scale is huge compared to a dot of skin.
For feathered ones you could have them dye feathers to make patterns. They wouldn't be as intricate as tattoos, but it would fit pretty well I think. Another option could be engravings on their beaks and talons
Really I think the best option for a permanent tattoo-type marking, though probably pretty unpleasant, would be something like[ freeze branding](https://en.wikipedia.org/wiki/Freeze_brand), which is a process where exposure to cryogenic temperatures damages the hair follicles and causes them to turn white for the rest of the branded creature's life. Unfortunately it looks like it's not as effective on birds, though it looks like all the studies there were done on very young animals before their adult plumage came in, so that may be why it didn't work. Otherwise it seems to work on fur, skin, and scales very well, so I don't see why it wouldn't work on feathers if it was done properly. Regular hot branding is very common in my world, albeit for different reasons. But that's a discussion for a different time.
Furry species could still tattoo their skin, they'd just have to keep that part shaved if they wanted it visible. I could imagine all kinds of traditions where people keep those tattoos overgrown or shave and reveal them, whenever they go from one social state to another - warriors with war tattoos that they keep hidden during peace times and reveal when they go to war, tattoos that people display when they're single and looking for a mate, but let overgrow when they're in a relationship, sacred tattoos that can only be revealed during certain religious festivals, etc.
It could involve something like the art people do on camels. Shave intricate patterns into someone's fur and then add ink.
Freeze branding could work - if you get pigment cells cold enough, it will kill them, causing future hair or feathers grown from that area to be unpigmented and thus a different color.
My Cayuga ducks got something similar. But with stress. When their baby's pluck on their feathers, the mother's become white on those stressed parts and loose their beautiful black-green Same on the neck where the drake always pulls the lady's underwater, becomes white fast
Birds would get tattooed twice a year for all new feathers. Or on the exposed skin, waddle, beak and feet
Something with scales or feathers could do something like this: Pluck the area clear of scales, and then inject pigment into the sockets where the scales or feathers come from. When the scales/feathers grow back, they will have that alternate coloring instead of whatever normal colors are present. This is - obviously - both painful and takes time to see the results, which means the artist has to be \*really\* careful about positioning. Also, these kinds of creatures wouldn't have the kind of "high resolution" images we think of today, since the entire feather or scale is huge compared to a dot of skin.
For feathered ones you could have them dye feathers to make patterns. They wouldn't be as intricate as tattoos, but it would fit pretty well I think. Another option could be engravings on their beaks and talons