St Helens Library do have the baptismal records for St Anne's Church, it was not named St Annes & Blessed Dominic till after the 1960's.
These documents are in the archives and you need to request that they be brought out, but they are written in Latin.
I found a lot of mine but you will need to sort out the names into English as well.
They demolished the old church due to mining subsidence and built a modern church (which by the way I hate) and they also demolished the lovely stone built grotto and replaced that in a totally different design to the original.
Because of my family connections with the original parish and the original church I do have a sliver of the the wood from Blessed Dominics coffin from when the opened it up the last time in the 1940's.