For the most part, the writing was signatures by the people involved in the final assembly of the two weapons at Tinian, in many cases including where in the US they were from. The bombs were painted with a sealant after assembly at Tinian, so the writing on them occurred once the paint had dried before being loaded onto the aircraft.

I do not believe there is any real proper inventory cataloging all the scrawls put on the devices, though there are a few close-up images in the archives showing some of these signatures/messages. In a few cases, there were a few short notes they included as well - in the pic above for example, showing a closeup of one of the rear stabilizing fins on "Fat Man", you will see the quotes "Here's to you!", and "lots of love!" included with the signatures.

Probably the most famous written quote that was well documented was the one written by Rear Admiral W.R. Purnell of the US Navy, where on the side of the "Fat Man" device while it was at Tinian he signed it and wrote the words "A second kiss for Hirohito!"