Ben, this thread has saved us from the hard way, I think. We've written to both our pension providers this week asking for letters that confirm the amount, the frequency and that the payments are for life, and asked for them in English as well as Swedish, since that seems to make the translation step easier. I'll report back on what the Spanish office actually accepts.
When we applied for residency here as retirees, we had to show that our pension income was enough to live on without working. I understand why. What I didn't understand at the time was how to show it.
We submitted bank statements showing the pensions arriving each month, and were asked for more: letters from each pension provider confirming the amounts, translated and certified, plus proof that the payments were for life. One provider took six weeks to send the letter. The other sent a letter that didn't mention "for life", which apparently mattered. It all got sorted, but it took three months longer than it needed to, and I'm fairly sure we did it the hard way.
For other retirees: how did you document your pension income for residency? Which documents did they actually accept, and is there anything you'd ask the pension provider for before you even apply?