"An bhfuil do chat tuirseach?"
Translation:Is your cat tired?
Is "black to black" an idiomatic expression equivalent to something like "night and day" in English?
Yeah, it's an idiomatic expression meaning 'all day' or 'from dawn till dusk'. Another idiomatic expression using 'dubh' is 'dubh le daoine' meaning 'crowded' or 'packed with people'. For example: bhí an áit dubh le daoine.
A phrase that is also commonly used in English in Ireland, though it doesn't travel well.
Does dubh dóite count as an idiomatic expression? I have it written down that it means "sick and tired".
You're right, it means 'sick and tired in the 'fed up' sense. Ó dónaill translates 'tá mé dubh dóite de' as 'I am heartily sick of it'. It seems one use of 'dubh' is to intensify a statement in the way 'downright' would in English.
Would "Tá tuirseach é i gconaí" work?
Edit: No, silly. It'd be "Tá sé tuirseach i gconaí"... I think...