If you don't already have a no doubt home run animation, go to the Community Market > Unlockables and filter by animations.
You can choose to buy the cheapest no doubt home run animation if you want or put in a buy order if you don't want to spend as much as what is already for sale (this will take longer).
Once you have your animation, go to Road to the Show mode and load your player, go to the Customize, then choose to edit your animations. Change the home run animation to the animation that you just bought.
Note: if you don't see the animation you have, it may be because the animation is for either one-handed, two-handed swings, left handed, or right handed. If that is the case, then edit your players swing to what corresponds to the animation you have.