Centaurs may not be able to reach all parts of their bodies but other centaurs certainly could. Put one centaur up on a platform (design it with a ramp) and another centaur can reach easily. Also, if they live side by side with humans, the humans can do things too.
Some real-life human decorations are such that you can not do them yourself. Or they are possible but very difficult and tiring, and hard to do well. Think: hair extensions, weaves, fancy hair braiding/styling (including with bells and such), hair cuts (including fancy shaves), hair dye, fancy nail care (think jewels and polish designs), piercings, tattoos, henna art, and much more.
In human societies, a lot of the above things are valued such that even people of low to moderate income still budget to pay someone for these tasks (like hair braiding every 3 months that takes 6 hours to complete).
I would guess that centaurs might do all of the above. The species-different stuff could include:
Henna designs on the flank.
Fancy dye jobs as well as braiding/bells/etc of the hocks and tail.
Shave designs of the flank.
Jewelry for tails (a bracelet for the part where the tail hits the body, or something woven in).
Piercings around the lower legs.
Most of these things would not need to be touched for days or even weeks. Just like a lot of humans now will wear a ring for years without removing it or will leave a piercing in for weeks or get their nails done weekly.