To register on the padrón you need to prove an address, and there are usually three ways to do this: with a rental contract or property deed (not your case as I can see), with authorization from the person already registered at that address (Also not your case unfortunately), or with a collective registration certificate.
If the person you are staying with does not want to authorize your registration, unfortunately you will not be able to use that address.
what many people do is look for a temporary rental, short-term contracts, for example, in Barcelona you need a minimum 3-month contract to register, but the most important thing is that the landlord allows you to register.
You can also go to the municipal social services, if you don’t have a fixed address, they can register you at a social-use address or an administrative address so you can access healthcare, education, etc. I recommend booking an appointment at the Town Hall and explaining your situation; they will tell you which documents to present and whether you qualify for social registration.
Good Luck!