To do this you will need to go to Settings.
On your delivery index page, click the delivery method you wish to edit.
Inside of the Deliveries area, head to the bottom of the page, where you will see a check-box labelled Applies to all products.
Deselect this to open up the Include / Exclude rules area. Inside the Include area, click the Add Rule button.
This will show the initial option available, which is to add a delivery to products in a certain category.
Click the left-hand dropdown, currently set as Category, to see all the options available. In this instance, we want to select Delivery address in (country).
In the right-hand input area, start to type out the country you wish to use, for example United Kingdom, and click the dropdown that appears. As this is included in the delivery, it will automatically exclude any other countries from showing the delivery method.
Finally click Save.
Now this delivery method will only display for customers who enter a delivery address with United Kingdom listed as their delivery country.