How do I find out what serif font is being used in the Day One mac app?
This application on the web helped me out a couple of times:

http://www.whatfontis.com/

Just take a screenshot of some words which are typed with a particular font (preferably with a big size) and upload the screenshot.

I am not affiliated with the site in any way, I'm just a satisfied user. Give it a try. Otherwise you could try to mail the developers of Day One.