OP,
I have some good news for you that just might help/inspire you to go back to your bank, but it must be your own branch to have any chance. It will probably depend on how much you are looking for however.
I have posted here recently on my personal debt woes (which were mostly due to career change/study). I only have credit card debts now having just paid off my car loan (it was a 5k loan- will not be changing my car for years so it was a long term investment and paid off now).
So even though this car loan is now paid off I still have the hangover of credit cards, the main one of the two is (well was!) 5.5k owing on my credit card to AIB.
Since I had just finished paying off my car loan (credit union) I was in a stronger position financially and so I went into my branch and spoke with a deputy manager and told her with total honesty what my situation was. As I have a graduate account the interest on a personal loan would be 8.7% compared with the 17.odd % on the 5.5k on my credit card and I told her I was making no inroads on my credit card balance despite paying in 180 per month due to interest and charges (I was a couple of months in arrears so was being charged with late payment fees also).
I told her honestly what my income is and that I could pay the 180 a month and she had initially said that you normally have to apply through the graduate loans centre so there was some resistance there, but I told her I had done so over a year and a half ago when I was in a better position and even then had been refused so I said I knew from that my only option was to speak directly to her/or the bank manager. She said she would speak to the manager for me and ring me later that day or the next day with the outcome.
So, I got word that same day that my loan was approved. They are transferring the money themselves to my credit card account and my new limit will be 500euro, rather than 5.5k but that suits me just fine as I am eradicating my debts slowly but surely, am almost finished my studies and ready for my new profession, and I will never get into credit card debt again.
So OP it is possible. Meet the bank manager/deputy manager, be humble and don't be afraid to show you're in distress because of the debts and be honest about your income and what you can afford to pay monthly.
This of course will depend on how much of a loan you need and you didn't say how much was involved. But hopefully this may help others in similar situation.