There’s a shop of crafts from La Palma beside the museum at Casa Lujan in Puntallana. It sells things like traditional embroidery and ceramics. In the centre of the room, there’s a traditional loom, although they didn’t have any rugs for sale when I was there.
(Palmeran rugs are made with a linen warp, and rag weft. If you order one, you generally have to prepare the weft yourself. That means cutting the old clothes into strips 1 cm wide and sewing the ends together, and winding it into balls. You need patience.)
They also have more modern arts and crafts, like this mobile by Rosa Vidal.
Open Monday-Saturday 10 am- 1 pm and 4 pm – 7 pm
Google map here.