Hi George
You live in a very different climate now and the pressures are much higher. Your coconuts have both fungal infection (the brown spots on the fronds) and insect infestation. The insects appear to be plant sucking insects (called hempipterans) which excrete sugar on the leaves and this has lead to other fungi growing. The insects often produce the fluffy material.

Although this all looks bad your plants might not be in too much trouble. They have lots of leaves and are making food. Plants can tolerate such foliar pests quite well. Before napalming the tree I would recommend a soil test to see if the soil is suitable for cocounts. If the trees dont have good nutrients then the stress is hard to overcome.

I would also suggest not spraying and encouraging local natural enemies that would eat the hemipterans.

Soapy water sprays are also a good way remove plant-sucking insects (as they have a waxy cuiticle and soap breaks that down)

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david