SAFE: apple
pear
hazelnut
yucca
cottonwood
beech
pine (dried, no phenol oils or sap)
manzanita (like parrot branches from pet shops)
cholla cactus (dried, available as chews and branches from pet shops)
DISPUTED: birch
ash
aspen
oak
juniper
AVOID:
citrus woods (orange, lemon, lime...)
cherry
wild cherry
plum
pine (fresh branches)
walnut
cedar
The difficultly would be using a wood that they won't want to eat too quickly.