Refused Credit card from BOI

It could be an automated decline. Which means it wasn't looked at and the computer just turned it down. I've was declined a loan with them despite clearing my previous loan early, a good credit history, job and savings. I went with another bank and got it within a couple of days. They seem to have a stricter lending policy then others. Try appeal it then try somewhere else.
You could try a visa debit card as they are accepted as much as a credit card.

Talk to someone in your local branch. I had a similar issue where they would have had no reason to refuse me but did anyways, a chat in-branch and they re-submitted my application with a supporting letter and I got one not long after that.