I believe "Would you like a put of tae?" would be:

Ar mhaith leat cupan tae?

First of all, am I correct so far? Secondly, to say "If you would like a cup of tea, please come inside" would be:

Dá ba mhaith leat cupan tae, tar isteach

How close am I, or any alternate suggestions.

cupán (síneadh fada)

dá ba - in Standard Irish: dá mba.

But ... it isn't really an irreal condition, so I'd think: Má bá mhaith leat ...

I Ros na Rún deirtear "ag iarraidh tae?"

Yes, in Conamara we use "ag iarraidh" for "wanting".

An bhfuil tú ag iarraidh tae? Do you want tea?

And we don't usually include "cupán", as you're more likely to get a mug anyhow

A Bhríd, would you say in general Ros na Rún is a good example of colloquial Connemara Irish?

If the character is a native speaker like Thadhg, then yes. And when Séamus and Peadar were there.
But I've lost touch with it for the last few years so I don't really know who the other characters are now so I can't say.

Bit of a necro post at this point but, going back to my original question,
Would ""If you would like a cup of tea, please come inside" be properly translated as

Má bá mhaith leat tae, tar isteach le do thoil.

And I assume that "cupán" is left out because it's assumed you meant a cup or some similar container.

You would have to use dá, not má in this case.

Hmm, níl mé cinnte. Ní léir sin, dar liom.
You can use má, too, with "ba mhaith"
e.g.: Ach má ba mhaith leat an sméar mhullaigh agat chuaigh tú go Meiriceá . (Ó Grianna)

Usually you use dá and conditional only in irreal conditions.
But it is not irreal here, at all. An imperative follows (rather impossiple in irreal conditions)
Conditional mood in ba mhaith is due to the modal meaning (= want) not because of irreality.

I'd translate dá mba mhaith as irreal "If you would like/want (but actually you don't like/want)" which is not meant here.

In case of iarraidh it is:
Má tá tú ag iarraidh tae, tar isteach (not: Dá mbeadh tú ag iarraidh ...)

But on the other side: I don't know.

Tá mé ar aon intinn le Labhrás.