Pressure treated wood really does not like to be painted, but it will take paint if some things are done first.
PT wood is green when purchased. It needs to dry out before you think about painting or staining it. Think of this wood as a sponge full of water, It will not accept any more water and will only if some is removed.
Pt wood is the same. In Texas, green PT wood will dry out in the summer months in about three months. That is 90 days of 100 degrees and over.
If you try to paint it when it is green, the water will still dry out and when it leaves the wood, it will take the paint with it.
When its dry, then prime it and paint it several coats.
I would like for you to consider pine or cedar wood for this project. It will much easier fit your schedule and no hassles.