you may be able to find someone researching the same lines on ancestry and then possibly copy any primary source material they have put on their tree. it's not quite the thing to do but if they are a distant relative it may work out. you can also find quite a few marriages baptisms or burials on county sites that might substitute from 1837, what county do you mainly need?
depends when you mean by further back, civil registration in Ireland didn't start as early as here nor was it necessarily as successful in bringing the nation into line! whilst it wasn't compulsory until the 1870s to use the civil registration system in england and wales, even after it was compulsory in ireland it was still hugely ignored or misled.