As a general tip, one of the things when I first started was having a partner who was pretty much at my skill level who was also good at ukemi. We would work after class on things like koshinage and would just alternate throwing each other for about an hour.
I don't know what "type" of koshinage you do at your school so it's tough for me to give specific pointers. If you can, grab someone willing and practice with them...
I guess that I'm constantly having trouble trying to lift my uke's center using my hips, I usually don't have a problem with the irimi, but after getting in position for the throw everything breaks up. My sensei makes it look so easy, especially performing the technique on the big guys.