Last year I got fed up of not having a credit card. Despite having a salary in blanco for several years, and then being self employed several years more HSBC refused to give me one. We tried several different banks without much success, before trying Santander Rio - based on a recommendation from our cleaner. The important thing to note is that apparently policy is not applied equally everyone. If you go to Abasto shopping centre, there's a santander rio in the basement. They have much lower standards for applications than other branches apparently. My partner and I were both able to open checking accounts with debit and credit cards, even though my partner has no tax ID or proof of income - a DNI was enough to open an account.
Can't tell you if this would work for you, but I'd give it a go.