Stable Care can be acquired in-game or on the launcher by using Star Coins.
When you log into the launcher, you see the icon of a horse next to your Star Coin amount. Click the icon and choose how many days you wish to get. Then click the purple button below and say yes to confirm or no if you do not wish to go through with it.
If you want to acquire Stable Care in-game, you can do it in two ways. You will need to go to your home stable, click on the noticeboard, choose Stable Care Help, or click on the top right-hand corner of the screen to see the number of days of Stable Care you have.
Depending on how many days you already have, you can choose between 1-30 days of Stable Care. The maximum you can have is 30 days.