Here are most of the words (admittedly slapdash) to the rest of the verses, as sung on the YouTube video linked above. Interesting, the way Tralee rhymes with 'valley'.

The Siege of Ennis is a well-known dance, I think. Is there another dance called 'The Feast'? That's what it sounds like in the next verse.
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For i met her in the springtime at a dance near banna's strand
to see her and her companions, they'd be dancing hand in hand
she looked so slim and lovely, in her dark green, velvet gown
and i fell in love with mary the pride of tralee town

if asked her if she'd take the floor and dance some steps with me.
we did 'the Siege of Ennis' and the polkas wild and free
her hair in long black tresses her shoulders sailing down
and i danced the Feast (?) with mary the pride of tralee town

the summer months we courted beneath the Kerry stars
we sang out all the old ballads in in the Ballybunion bars
by the cattle green we wandered, the silver moon being down
when i kissed my darling mary the pride of tralee town

the golden leaves of autumn gave way to winters cold
and another came a-courting her and he stole her heart of gold
for he had many acres and the cowlands all around
and it went ---------------- Mary the pride of tralee town

So farewell my good companons I take the morning train
i'm bound for south australia and you won't see me again
he's a richer --- and a better man, so the tears come tumbling down
what a -------------------- is Mary the pride of tralee town