Gran canaria?

Hello! where on these god forsaken islands can I get a decent diaper?
Carrefour has Some rubbish, but jesus, some store must have tena/moli/abena?

You are likely out of luck unless you can get something shipped to you. Truthfully your most cost-effective solution would be to order in bulk. Not regular bulk, but this-needs-a-small-container-bulk. Places like alibaba.com go to great lengths to get their advertised products around world-wide, your island included. The catch is that they have minimum order quantities which is why bulk refers to ordering a small container; additionally the product typically doesn't get to you for some time due to shipping by slow boat and customs, so be prepared for duties to be paid too.

I hope I answered your question, even if not satisfactorily.

I've never been in Canarias but I'm from spain. Guessing that's still the same countries with the same laws & stuff you should find "quality" diapers in any pharmacy. People say that the pharmacist will ask you questions, but he/she doesn't if you are just direct: Brand + Absortion + Size. The only drawbacks are that you have to ask someone personally to get them for you, and you can't buy less than a box (~80 diapers)

My favourite brand in spanish pharmacies are ID slips (before they were Tena slips until they changed).

It's even better if you try to find the national code, call the pharmacy a while ago asking if they have this specific product, and then go buy it. It's hard to find these numbers but they can be found online, for instance ID Slip and a general -but a bit outdated- list

And don't cheat, you don't have prescription, that's Ok, you will just pay the whole price of those diapers. I've been in three different pharmacies so far, and while all three asked me if I had any prescription, they didn't put me any problems when I said that I don't, but I will pay the whole cost.
Keep in mind though, that in some pharmacies they could just decide not to sell them to you.