...I wouldn't say that I KNOW 365 songs ...
There are two books that you could mine for material both 'Daily Ukulele' and 'Daily Ukulele: Leap Year edition' by Jim and Liz Beloff.
Each book has 365 songs made easy to play for ukulele. There is also a baritone version.
Most of the songs are in the key of C or G, and easy enough, and every song includes the chord pictographs at the top of the page, as well as the melody line on a staff of standard notation, with the chord changes indicated.
see here: http://dailyukulele.com/