Coins can be purchased from the Golf Clash shop. To purchase coins simply select the shop icon from the main menu screen and then scroll down to the "Coins" section. You will then be able to select how many Coins you would like to purchase.
 
Or 
 
Select the plus icon on the top left hand side of the game window where it is showing you how many Coins you currently have. You will then be able to select how many Coins you wish to purchase.