OK, this is going to sound really weird, but it works for me.
Years ago, the fashion was to paint scads of eyeliner on our eyelids. I could never get both eyes perfect. I'd wind up looking like Cleopatra in one eye and Kiss with the other. Drove me crazy till one day I read this fashion tip:
Open your mouth.
Yes, open your mouth,
because when you open your mouth, it somehow relaxes the eye muscles. At the same time, it steadied my hand.
And it worked like a charm!
So now, when I have to relax and get that IV, I open my mouth.
Isn't that the craziest tip you ever heard? But I'm one of the best IV sticks on my unit, so don't knock it till you've tried it.