I think most people agree that
Fadhb ar bith* (on it's own) is Béarlachas, but the more natural alternatives aren't always clear.
Ní fadhb ar bith é sin exists as a sentence but dropping the
ní changes
ar bith from "no" to "any". Adding
gan doesn't really solve the problem either.
So what do native speakers say? It depends on the context. Focloir.ie offers a few suggestions
here.
Borrowing and elaborating on some of their examples:
Expressing willingness to do something:
"An ligfidh tú amach anseo mé ?" "Cinnte." "Will you let me off here?" "No problem."
Cinnte is literally "certainly."
You can also use
agus fáilte:
An déanfaidh tú dhom é? "Déanfad agus fáilte""Will you do it for me?" "Yes, with pleasure."
Reply to thanks:
"Go raibh maith agat as an gcabhair." " Fáilte romhat."/"Tá fáilte romhat.""Thanks for the help." "No problem."
"Go raibh maith agat as do chuidiú." "Go ndéana a mhaith duit.""Thanks for the help." "No problem."
Tá fáilte romhat/fáilte romhat is "You're welcome"
Go ndéana a mhaith duit. is another way to say "You're welcome"
Reply to apology:
"Tá brón orm faoin moill." "Ní dada é.""Sorry about the delay." "No problem."
Ní dada é means "It's nothing."
(You can also say
Ná bac leis. "Don't bother about it." or
Is cuma. "It doesn't matter." in reply to an apology.)
Some other ways I have found to say "It is no problem/bother/trouble (to do that for you)":
Ní meáchan ar bith orm é. "It is no weight on me."
Ní stró ar bith é. "It is no trouble."
Perhaps others have some suggestions for the different contexts? ...