Can I change the colors of my Google appointments as they appear in the Coaches Console?

The color of your Google calendar events is setup on Google's end, where you can go and change the color of the respective Google calendar from its settings. The Console system displays the Google calendar with the same color as the one you setup in Google.

Please keep in mind that the different colors you might assign to your various events in the Google calendar (event color customization) do not translate as such to the Console calendar. In the Console calendar you will see all the Google events with the main/default Google calendar color.