I'm not trying to insult you, but try googling how to "string a guitar'. There are a couple of things I learned from doing that even though I had been playing for years. So, make sure you are stringing the guitar correctly and stretching the strings. Some people have also swapped out the tuners for locking tuners.
When I got my 59, I thought I was having tuning and intonation problems. It turns out, I needed to lighten my touch. I was used to playing an Ibanez with low action and low frets. I found that the JTV's frets were higher off the fretboard. So, when I was fretting a note, I was pushing the string all the way to the fretboard and causing the note/chord to drift slightly out of tune.
This got worse when I tried a set of nines for strings because they were so slinky.
If you swapped out the tens for nines, try to lighten your touch on your left hand and see what happens. It takes some time to change your technique, so I put tens back on and that helped.
Find these vids on you tube: Gibson Guitar Tutorial: Joe Walsh - Guitar Setup
Joe shows how he sets up his guitars and keeps them in tune. It's also a great tutorial for learning Joe's guitar face!
jpmull's post in Jtv 59 Wont Stay In Tune was marked as the answer