One of the drills that I did to learn giants was just simply high tap swings that eventually pulled over the bar--yes, it's possible to do a giant from a tap swing--it just doesn't necessarily pass through handstand.
When learning a giant there are going to be times where you don't make it over the bar and fall back down--when this happens, just treat it as though you casted over the bar and let go of the bar and fall to your feet. It's really not as scary as it seems, but something you can do to help have a coach spot kip cast handstands that fall over the bar.
Most importantly, you've got to believe in yourself. Your coaches wouldn't have you learning how to do giants if they didn't think you were quite capable of doing them safely. Gymnastics is partially about taking risks and overcoming challenges--there are going to be tons of skills that you're going to be afraid of doing (at first of course) but as you do them you'll gain the confidence. Sometimes you've just got to make yourself go for it. Decide before you get on the bar whether or not you're going to go, and once you get on the bar count to 3 and just do it.
Giants are really fun skills--they're kind of like rollercoasters--as you swing down you're going down the hill of the rollercoaster, then at the top it's like being at the top of the hill.