According to BOC No. 112, published on Wednesday, June 2, 2021, it is no longer mandatory to have an antigen test in order to check in to a hotel or any other touristic accommodation in the Canary Islands, if you can prove that you've recovered from the disease or you've had your vaccination.
So, according to this rule change, which applies for people over the age of 12, in order to stay in hotels, touristic apartments, or licensed villas, you will need one of the following:
Check the official BOC document (it's published only in Spanish)
Update from June 24
The Governing Council agreed on Wednesday, June 23, to modify the conditions of access to tourist accommodation in the Canary Islands for visitors who do not reside in the archipelago, which will no longer require tests in the case of kids under the age of 12; up until now the age limit was set at 6 years, so now it has been extended to 12. This means that kids under 12 will no longer need a test in order to stay in touristic accommodation in the Canary Islands.
Although Spain had already announced that it will start receiving tourists from the UK without the need for tests or vaccination certificates in order to enter the country, the Canaries still maintained in place until now the rule according to which you would need an antigen test in order to stay in licensed tourist accommodations like hotels or licensed apartment rentals and villas.
With this change, visitors from foreign countries, who have either receiver their full vaccination scheme against Covid-19, or who have received the first dose at least 15 days prior to arrival, or who can show that they have already recovered from Covid-19, can check in to hotels or any other accommodation, without needing an antigen test.