i want to apply for z visa in dublin, so how i should do it?

I have Lithuanina passport and I'm visiting my mother in Belfast. I have invitation from china for z type as entertainer. Can i do it in dublin and how long it will take? I can go to dublin just once, so if they accept my application, can they send it to my adress or it will be done same day, or i have to pick up it, my self? and how i can pay if i dont have Ireland bank acount?