Did it peel down to a previous coat of paint or to the bare wall? Are the walls plaster or drywall?

To see if a paint is oil or latex apply so GOOF OFF on a rag to the paint and if it softens and gets tacky it latex and if not oil based.

Did you clean the surface first? Peeling paint is sometimes caused by that. Then use a 100% acrylic primer to stick to and hide the old green color. Ceiling paint is not designed to do that. Behr makes one called Enamel Undercoater. Prime, then texture, then paint.
Most builders never prime walls or ceilings. Did the green color peel off, too?
Good luck.

If this house has a fireplace this will be your #1 place to think about,heavy smokers will cause it too.Smoke left on a ceiling will do this same thing every time.As 5 said too if you are using latex over oil this can do this.You can use oil over latex but never latex over oil.The latex won't stick (what you are experincing) but vice versa oil will stick to the latex.
Deford I am a painter I have never heard of a builder (Contractor) ever painting a house.
They always get subs such as me to take care of this,and if someone is painting bare walls and ceilings without primer they will not be in business very long.They also need to back roll,besides this most ceilings are primed by the drywaller when they texture or orange peel it.

The walls are plaster. And yes we did clean the ceiling first before we attempted painting. The bubbling paint that peeled off was mainly just the top white layer that we had just put on, there was a greenish tint on the back of it, but not actual green paint chips.

Also we do not have fireplace and the previous owners were the original owners and they did not smoke.

Thanks for everyone's advice and tips!!!

Hi! I recently had a similar situation. On one wall of my bedroom, every time I would try to paint it, the paint would peel off, or sometimes it would not stick at all. I cleaned the wall thoroughly many times, but that didn't solve the problem. By sanding the wall, I realized that the only paint that stuck well to the wall was the contractor's paint. I tried Benjamin Moore's Sure Grip, Para's Super Stick, Glidden's Ultra Hide Gripper, none of them worked, but Zinsser's BIN worked just fine. Then I painted over it with my finish paint, with no problem. I would suggest that you try it on your ceiling, after thoroughly cleaning and then rinsing the "non-stick" area. Hope this helps you!

Im thinking that being plaster and a green color,sounds like it is from the 70's?
If so 90% sure that it is oil and is why it is not sticking and bubbling because of the difference of chemical compostion make up of the 2 paints yes zinzer primer should do the trick.

I work for a paint manufactuer (Duron) and want to get rid of a myth. If you do not prime a bare drywall wall before you paint the paint will not peel off in sheets as some say it will. If this was the case there would be thousands of houses with this problem as 90 percent of the homes in my area ( Central Virgina) are not primed before they are painted. The primer does give you a more sealed surface on which to paint and the finish paint will look more uniform and even and this especially true if you are using a finish with a sheen. We have mostly smooth wallls here and there are primer/surfacer products we are selling to hide the defects in the walls as the finishers are doing a very bad job of getting the walls in good shape to paint them. Also you back roll the paint on the walls only to hide the defects in the finishing and to aid in touch up.

5 I would never paint a house without priming it 1st,unless it is a flat based paint,90% of the problems are from people trying to paint without using a primer.As far as back rolling we only back-roll the primer this aids in sealing and penetrating into the holes in the rock,anyone who does the actual painting will know that the drywallers cannot get rid of all pin holes air bubbles or all imperfections,when I am doing multimillion dollar homes I would never paint without any primer,if you are back rolling your top coat then yes you are probably trying to hide something but we never have to from back rolling the primer.I would never touch a house with just spraying a satin top coat.Im busy enough to refuse it,is not worth taking the risk.
I know their are products out there that can be applied 1 coat and is a very heavy,high hiding product,but as far as a finishing the drywallers from where im at better have everything taken care of cuz our jobs is to paint not fix,but I do small repairs and such that may be missed.Im not 1 of these it's not my job to sand or do it so im just going to let it go,im the last one to leave a house and im going to let a small imperfection ruin what you see when im done.
In all fairness to everyone on a new 7-10 thousand square foot home,or a comercial job something usually has to be touched up or fixed.