It will depend on where in Spain, as that is regulated by local government (autonomías). You should ask the local municipality (ayuntamiento) for an authorization, and you will probably be required to pay some form of tax.
I've been trying to find an authoritative source but, as Spanish government is so decentralised, regulation is so fragmented that I couldn't find any.
Edit after clarifications
Regarding the Canary Islands. Autonomic regulations in the Canary Islands can be found here. The link is a bit old and in spanish, but I could not find anything newer. From what I could gather elsewere, it is still current.
The relevant part is article 6
Artículo 6. En cualquier caso, cuando se trate de acampadas en montes
de particulares, el propietario de los mismos o aquellos que deseen
acampar con permiso de la propiedad, deberán solicitarlo a la
Viceconsejería de Medio Ambiente con una antelación de diez días.
Which means that if you want to camp in a private property, the campers or the land owner must request an authorization to the environment administration at least 10 days in advance.
Contact information (in Spanish)