Help Center

In order to give rosettes, your competitions will need a very high prestige, 75% or more. This means they need to run regularly and have participants with high skills.
If you want to increase your competitions prestige you can try always signing up two of your horses, to help them running, and slowly increasing the difficulty, to get skilled participants. Of course, if you want to use this method to get rosettes in your ec, you will need to own horses with high skills to match your competitions difficulty.

If you need advice that's more specific to your competitions and situation, you can try posting in the game play forum, where you can give more detail and people can see what's going on with your competitions :)