I am sorry to interrupt your learned discussion with an ignorant question about the use of h on nouns after numbers. I am just trying to help my son learn Irish
According to his Irish book, coinin goes to choinin after numbers 1-6 and then goes to gcoinin after numbers 7-10
Dha choinin, tri choinin...seacht gcoinin etc

Should he also put an h after cat, carr and madra on 1-6?
ie dha charr, tri chat etc.

I'm using O Se's teach yourself, and that seems to hold true for most cases. So I say go for it.

(And if a word is irregular, it'll usually say. Look for words like "a special form," or something to that effect)

O Se's is the "standard," though, so I have no clue how that works out in terms of the different dialects.

Your question isn't ignorant, it's intelligent if anything. We were all a beginner at one stage (contrary to popular belief).

Here's the rule:

1 to 6: séimhiú
7 to 10: urú

aon pheann
dhá pheann
trí pheann
ceithre pheann
cúig pheann
sé pheann
seacht bpeann
ocht bpeann
naoi bpeann
deich bpeann
aon pheann déag
...
sé pheann déag
seacht bpeann déág
...
sé pheann agus seachtó
seacht bpeann agus seachtó


As for "special" or "irregular" nouns when counting, there's very few. However here are the main one's:

bliain: aon bhliain, dhá bhliain, trí bliana, ceithre bliana, cúig bliana, sé bliana, seacht mbliana, ocht mbliana, naoi mbliana, deich mbliana

ceann: aon cheann, dhá cheann, trí cinn, ceithre cinn, cúig cinn, sé cinn, seacht gcinn, ocht gcinn, naoi gcinn, deich gcinn

Also parts of the body (the hand, the ear):
(I'll admit I'm not 100% on this one)
aon lámh, dhá lámh, trí láimh...
aon chluas, dhá chluas, trí clúise

On the irregularly-counted nouns, I have a webpage where they're all listed and explained:

http://mbm.dotnet11.hostbasket.com/textmachine/Default.aspx?PageID=89

Hopefully you'll find this helpful.

A slight complication with those, in my humble opinion, is that the counting system of Irish is continually changing towards greater regularity, and many words which used to be counted irregularly one or two generations ago are increasingly being treated as regular now.

Perhaps somebody with a better understanding of the historical development of Irish would be able to give us more information on this?

"counting system of Irish is continually changing towards greater regularity"

you mean more like english with numbers in decimals not scores, and less mutations...

I'd like to see more of this modern/post modern irish from young speakers emerging. If the genitve and weak plural are gone that is one thing -stong plurals and simple word sequnece in their stead, but if pronouns (like in Mayo) most all collapsed to /@/ for his, her, our, yier, they becuase one could rely on lenition or eclipses. If these disappear, what does one do? That would be interesting