I've been studying PUL's cork bible translation side by side with an old Douay-Rheims that I have.

I have one of those "An Bíobla Naofa" that were printed with unfortunately small text, but I decided I'm not going to let them stop me anymore. I was wondering if anybody knows an English translation that is close to the ABN, as the Douay -Rheims doesn't seem to be.

Hey, that’s really interesting! I think what you’re noticing is that different Irish Bible translations have slightly different approaches to phrasing and style. An Bíobla Naofa (ABN) tends to be more modern in language compared to the Douay-Rheims, which is more literal and archaic English.
drift boss
As for an English translation close to the ABN, there isn’t an exact match, but some people find the New Revised Standard Version (NRSV) or the New International Version (NIV) captures a similar readability and flow in modern English, even if the wording isn’t identical. It might also help to look at parallel editions side by side to get the nuances.

It’s great that you’re keeping at it despite the small print that kind of dedication really helps with learning both the language and the scripture!