Replace "Continue reading" link with button in Coraline theme

Hi, I have searched for this information but I think Coraline has some peculiarities that are confusing me.

I’d like to replace the “Continue reading” link seen on posts on the front page with a custom-made button that I’ve uploaded to my images library.

I’m not sure what template I need to edit, or what I enter to make the button appear.

Any tips gratefully accepted!