Donkeys are great little harness animals. They have been used all around the world for transport, and are very willing animals with the right training. Although they are stereotyped as being stubborn, that is because people try to treat them like horses, and they are not horses!!! There is a famous quote about donkeys “Stubborn? no, just smarter than your training skills”
The temperament of your animal is important. A friendly willing-to-please, calm animal is essential. I would not recommend taking a feral animal with no handling and trying to make them into a show animal unless you have a lot of experience and skill.
To start with you need to do lots of ground skills first, so they are confident in you. They need to know you will not harm them or put them into unsafe situations. Obstacle and agility work and de-sensitisation to scary things is a good starting place. Then you can introduce small changes and eventually build up to attaching the cart.
When I got my first donkey I had very limited experience with harness, from when i was a child 30 years prior. So I took things very slowly. First I got him used to having a bridle on, and did some long reining ensuring the ‘stop’ command was well practiced and effective. Then I attached a quick release rope to a tyre so he got used to the feel of something dragging behind him. Then I attached a home made sled that was quite heavy, which made the ‘stop’ command easy to comply with. Finally I attached a cart and got him used to the feeling of the britchen strap pushing against him when he stopped, and finally I hopped into the cart and all went well. I am now able to put him in and out by myself, but it is definitely easier if you have someone around in case something goes wrong. If you are not confident in your own skills, I would recommend sending him to a trainer who has the expertise to do the training for you.