-- You've got the right idea with the soothing words and patience. Let's take a look at things from his point of view shall we?

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If I were to play favorites in the bird world, this bird would win every time. Although I love all of the hundreds of rescues my animal care org handles and I specialize in macaws, my first love was a ‘tiel and we currently have about 30 between two lifetime cockatiel owners.
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One of my favorite websites for ‘tiel info is

http://www.letstalkbirds.com/cockatiels.htm
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When I advise anyone about ideal bird care, first it’s about the cage. Be sure you offer the largest cage possible that’s appropriate for your type of bird. Just like you’d like plenty of room in your home, the bird needs space too.
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Be sure the bars are properly spaced (they should not be able to poke their heads through them) and that the cage is of the right material.
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Never put a bird in a cage with rust and never trust a newly painted cage unless you’re absolutely sure it’s a bird safe paint. Paint products that are child-safe and say so, are usually bird safe; however, they must dry thoroughly, at least several days and then be washed down - before being ready.
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I’d approach our new additions (usually abused birds entering rescue/rehab) an hour or so after tucking them in for nighttime. Their cages are covered on all sides, leaving just ½ of the front uncovered so they can see out and feel secure. It also insures decent air circulation. The room light would be very dim, but not totally dark. Most birds have poor night vision, unless they’re nocturnal birds like owls and approaching them in total darkness is frightening to them.
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At this time, whispering, putting a hand up against the cage and just holding it there is a start. Remember, keep it non-threatening and below their eye level.
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When you notice them calmly stretching a wing and leg slowly out to the side and back, mimic the action with your own arm slowly stretching out to the side and softly stay engaged vocally (“what a good bird you are”, “that’s a pretty bird”, etc).
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After just a few minutes of nice interaction, leave them be for their night and the next day use the same tone of voice and slow, calm movements around them.
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Open the cage door (as long as your bird is not panicking and will be safe if they escape, unable to get to places you cannot recover them from) and offer your finger/hand just above the feet and gently touching at the breast area there say “step up”. This command is important to use every time so that when the bird hears it they know it’s time to be on hand/finger.

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In an untamed bird there may be some biting and squawking, but if you can tolerate it until they are on hand, you’ve accomplished a very important step. Once up they usually stop biting where they’re perching (your hand) and if they don’t, giving them an “earthquake” a gentle shaking of your hand, but not enough to dislodge them or cause them to feel insecure, will often distract them.
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I’ve also found that walking quickly into a different room (which isn’t hard to do with a big macaw chomping down on my arm like a pitbull) will surprise them enough to stop. Suddenly, in new surroundings, I’m their best friend.

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If you cannot get your bird to cooperate right away with hands, remember, you’ve got years ahead of you – it’s worth it to do this right. Try just placing your hand in the cage for a minute and letting them get used to it being there. Having a treat in hand will help make your fingers a positive thing.
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Continue the night whispering and no matter what, don’t give up.