I would tell my teammate to play APEX LEGENDS to train their hand eye coordination skills. It's a fast paced battle royale game with a lot of movement and aim needed to be successful - aka perfect for training some hand eye coordination. Either playing on keyboard and mouse, or using a controller, you have to be able to time up movements and inputs well in order to execute successfully in the game. It takes a lot of practice, but it does improve your reaction time and coordination skills.

Otherwise, you could just do some strandard tennis ball catching training or something like that. Isn't that what goalies do to train their hand eye skills? I'm sure players could do that too, have a trainer toss tennis balls at them randomly to improve their reflexes and coordination. If that doesn't work, there's no hope for my teammate. Maybe being a coach is the way for you in that case.