How can I exclude specific SKUs from coupons?

From your Magento dashboard, first go to to Promotions > Shopping Cart Price Rules. You can choose an existing rule to edit, or create a new one. 

On left sidebar, click Conditions >  +  > Product Attribute Combination > + and then select SKU from the drop-down

Choose the parameters and then set the SKU value. 

You can add as many SKUs to exclude as you'd like! If there are too many SKUs to limit, you can make this rule to apply to categories, instead.