Ivy I wouldn't of thought would be a good idea as ivy up any tree isn't good!
Clematis would be worth a try, and perhaps one that you cut down at the end of each year so the crown of the palm doesnt become thick with brown twiggy clematis stems

Ivy is a no no, as Nicky says above. Clematis (use a viticella or jackmannii variety, these can be cut down) will need some kind of netting or mesh to climb up - you'd have to wrap the trunk of the tree in it for the clematis to climb on its own.