Actually, Marion, there is a song called "Molly Malone" that's totally different from Cockles & Mussels. So far I haven't added it to my playlist though. (I have sheet music but haven't learned it.)

I'm going to try to learn Si Bheag, Si Mhor -- at least instrumentally, if I can't master the Gaelic.

My partner and I will also be doing Both Sides The Tweed (No tomatoes. I know it's Scots. Sue me.) and Dear Old Donegal, If You're Irish, Come Into The Parlour, and a few other "faux Irish" songs that will go over well with our audience.

And, Mark, I didn't even notice you asked for chords for (the dreaded) Danny Boy.
A bit late, but I really like these chords (though I capo up 2):

[D]Oh, Danny Bo[G]y, the pi[Em]pes, the pi[G]pes are ca[C]lling [Am7]
From gle[D7]n to gle[G]n and do[Em]wn the mo[G]untainsi[A]de. [D]
The su[D7]mmer's go[G]ne and a[Em]ll the ro[G]ses fa[C]lling[Am7]
'Tis y[D7]ou, 'tis y[G]ou must g[D]o and [D7]I must b[C]ide,[]G

But co[D7]me ye ba[C]ck when sum[Am7]mer's in the me[G]adow[Em]
Or wh[D7]en the va[]Clley's hu[Am7]shed and wh[Em]ite with sn[A7]ow. [D]
'Tis I'l[D7]l be he[G]re] in sun[C]shine o[D7]r in sha[G]do[Em]w.
Oh, Da[D7]nny Bo[G]y, Oh, Dan[G7]ny Bo[C]y, I lo[Am7]ve yo[D7]u so[C] -> [G]

(I don't do full chords in all those places where I have chords indicated, Some are walkdowns and individual interim notes. But it works with the full chords too.)