Bill, you made me rethink my statement. All those who hate statistics and probability please skip my contribution. For all other, here you go:
Assume that chance is the only operating factor (noteworthy events are distibuted evenly across the year; and forget please about the 29th of Feb.), then it boils down to the question: How many songs mentioning dates must exist that the probability that each of 365 days is covered at least once is higher than 50%. This question was too difficult for me and our statistician (we both can in principle write a program to find the solution, but we couldn't think of an easier way). To give an idea, how high that figure is, imagine you had already found songs for 364 days. How many additional songs mentioning dates do you have to find in order to have a 50% chance of covering the last day? It is 253 additional songs you need to have a toss-up chance. My rough guess is that you need to find several thousand songs mentioning dates in order to have a fair chance to have a song for each day of the year.
Now the assumption of chance being the only factor is definitely wrong. Whereas, for instance, pit disasters might be evenly distributed across the year, shipwrecks aren't (for storms aren't). In addition to that, songs covering the same event usually mention the same date (not necessarily true, for there are songs that cover the same event but do not mention the same date, see for instance the thread "Who laid the charge in Dublin City ?????"). And furthermore, the authors of songs will find it more easy to incorporate some dates into a song than others (If I had the intention to write two songs on two disasters that happenend on May, 5th, and on December, 28th, I probably would write "on that fateful fifth of May", but "on that bleak december day").
All these factors will lead to an uneven distribution of dates mentioned in songs across the year. The consequence is that you need to find more songs in order to cover all possible dates. Once more a very rough guess and the bottom line:

If there are more than about 10,000 songs mentioning dates then the probability that there is a song for each day is higher than 50%. Could that be possible? I guess it could.

Sorry, Bill, for using your post for digressing into probabilities. Your main point is well taken. There are so many more songs than the ones already in the database, that it would be fairly easy to find find songs for most days of the year. Perhaps I should have a look in my book "Songs from County Clare" with a lot of sports events songs to contribute some dates that are not covered in your shipwrecks from Wexford.

Wolfgang