There is a trick to opening their little mouths.
Hold the head by the bones around the ears tight enough to prevent head movement. I use thumb and index finger on one hand. I wrap the little dragon in my hand lightly enclosing with my fingers. The little finger underneath to prevent backing up and escaping.
With the edge of the syringe (when you get the trick, start with a fingernail first) catch the top of the lower lip right in front and pull gently down, then relax, then pull, then relax. If you just pull they will clamp their mouth shut and it won't open. It sometimes takes 15 of these pull, relax cycles to get it to open enough on the stubborn ones. I do about a half second per cycle. So in a second (you know "onethousandandone") I pull about twice.
Once you get the hang of it, it's not nearly as traumatic on the lizard, or on you.
We have one that has figured out we are going to feed her no mater what she wants, so once she realizes she can't get away from it she just opens her mouth and eats right out of the syringe. Good girl!!! Wish she would teach that to our little sick boy.
Be warned they do have teeth, and one of ours is not afraid to use them biting the syringe (or fingernail) with a vicious look.
Make sure and love on them when they eat from the syringe. It is traumatic enough to have food forced on you. Don't want your Dragon freaking out at the sight of a syringe in the future.
