According to Lonely Planet's Canary Islands Travel Guide, 4th edition, p. 31:
Although the term Canario has come to designate all of the islanders, it once referred more strictly to the people of Gran Canaria alone (now more often as not referred to as Grancanarios or Canariones). The people of Tenerife are Tinerfeños; those of Lanzarote are not Lanzaroteños but Conejeros; Fuerteventura, Majoreros (from the Guanche name for much of the island, Maxorata); La Gomera, Gomeros; and El Hierro, Herreños.
Unfortunately, this text misses Isla de La Palma, whose inhabitants, I believe, should be named Palmeras (f) and Palmeros (m).