It'd be much easier to list things they CAN'T have
Iceberg lettuce: mostly water, can cause runny poops. Romaine lettuce is okay.
High amounts of spinach, parsley, turnip greens and beet greens: contain elements that prevent proper absorption of calcium
Avocado in ANY form: Deadly
Anything high in sugar: Unhealthy
Anything with caffiene: Toxic
Anything with alcohol: Toxic; can severely damage the liver.
Pits and seeds from fruits: Many contain small amounts of things like cyanide. Toxic.
Dairy: Cockatiels are lactose intolerant; they can, however have plain yogurt.
Grit: Like oyster shell, sand, gravel, etc...unnecessary, can cause crop impaction. Calcium can be obtained through crushed egg shells, mineral blocks and cuttlebone.