I'm not quite sure what part of the verb this is - tharraingítí
Here's the context -

Bhí rí ramhar ann,
Is ba ramhar an rí é.
Tharraingítí síos é,
Is tharraingítí suas é, srl

Past habitual ("used to" tense) autonomous (unmentioned agent, usually translated "they" or "one"). "They" used to draw/pull him down.

_________________
The dialect I use is Cork Irish.
Ar sgáth a chéile a mhairid na daoine, lag agus láidir, uasal is íseal

Go raibh maith agat - would it be in dialect as I haven't been able to find it?

The uninflected form of the verb is Tarraing (or Tairg in some dialects).

_________________
The dialect I use is Cork Irish.
Ar sgáth a chéile a mhairid na daoine, lag agus láidir, uasal is íseal

tharraingítí is standard

It's a little different in Cork Irish:
http://corkirish.wordpress.com/verb-con ... arraingim/

Go raibh maith agaibh - I finally found it - I hadn't been looking in the right place.
par contre, in the next part of the rhyme there is a dialect form of a verb -déarfadsa.

Beo idir chapaill é,
Is marbh idir dhaoine é,
Is más gearr leat mo scéalsa,
Déarfadsa arís é.

He's lively amongst horses,
And he's listless amongst people,
And if my story is short to you,
I'll say it again.

* I just thought I'd have a bit of fun translating this. *

I thought it meant that he was dead, which is why the story gets cut short, but never mind. Anyway to say this rhyme properly you have to have that ultimate fashion accessory sitting on your knee, just waiting to go up or down, according to what you're reciting to it ie- a baby. If you haven't got one handy there's not much point really.