It's not uncommon to tip those in service industries like hair stylists, restaurant servers and valets. In some cases it is expected. But do riding lesson coaches or instructors get tips?
I've never heard of anyone tipping an instructor or riding coach. I would ask around your stable if it is common practice in your area. Maybe it is in some places. I do know that riding instructors and coaches are recipients of gifts at special times of the year--like Christmas or birthdays. But these are not obligatory.
If your riding coach attends shows with you, you’ll pay extra for that and in some cases have to supply lodging and meals. There may be other expenses for riding coaches that offer services outside of regular lessons. Be sure you talk to your coach beforehand to avoid any expensive surprises.
What riding instructors and coaches really appreciate are people who are on time (early) for their lessons, dressed and ready to ride, with an enthusiastic attitude. A big smile and a thank you at the end are always appreciated too