They could potentially file the suit against Spain in European Court of Human Rights if they have exhausted national remedies. ECtHR has previously ruled some blocks to be illegal, but generally in the context where country sought the ban. Of course in both cases Court is the one that actually orders the ban.

One relevant would be Yildirim v. Turkey where court ordered blocking access to all Google sites because there was one that where someone insulted the memory of Atatürk. This was due to request from Telecommunications Directorate. This then caused the appellant's website to get blocked as well.

Another one would be Vladimir Kharitonov v. Russia.