Ignoring most of what's above, there aren't many songs that address the famine directly, particularly not from the time. Skibereen is a useful pointer on the general position of the Irish farmer, but not too famine specific. While it mentions blight, it's more concerened with land tenure and eviction than starving.

The fields of athenry is one of the most specific, referencing Trevelyan by name.

Most of the songs about the difficulties of living on the land - The Sky Road, Leaving the Land etc - could as well be about Australian or American farmers, or those anywhere else.

A few emigration songs reference the famine - Shane McGowan has a great line about "fear of priests with empty plates" in Thousands are Sailing, and as mentioned above City of Chicago covers similar areas.

I can't think of any not mentioned that specifically address the famine.

One thought that occured is that a search through the Gaelic tradition might yield you better results.