Okay, you're going to have to spend a lot of time with him, to help him learn how to have a motionless sleep. At night, his brain switches gears and he sleeps fine.. but during the day, his body has difficulty settling from an awaked state to a sleep state, on it's own-- which is why he has a great sleep in the swing-- it soothes him to sleep and keeps him asleep. It has become his day-sleep association.
So, to change this, you're going to have to clear your schedule for about 3 weeks (it takes the circadian system 3 weeks to reset), and really support him to sleep. Remember how Tracy says that you have to stay with your baby a lot when they are learning how to fall asleep/stay asleep. You will need to do this.
Come up with a predictable wind down routine. You're going to start decreasing the swinging time. Move the swing into his room and darken his room. Time how long it takes him to fall asleep in the swing and take note of it. This will be your "baseline" for how long he will swing for.
Then for subsequent naps,(make sure the room is dark first) swing him just to a relaxed state, making sure it's not as long as his "baseline"-- before he starts to open and close his eyes (you know how Tracys says about the stages of falling asleep-- in first book-- you want to get him by stage 2). Quietly and very low key, take him out of the swing while he is still relaxed and awake, do Tracy's 4 s wind down routine, and the lie him down when he is "ready" (drowsy but awake). If he starts to cry, then do pu.pd.. making sure you are doing it properly so review pu.pd chapter. Whatever you do, do not put him back in the swing. Just make the swing part of your wind down routine.. not as a last resort.
You're going to have to stay with him during his naps. Since he's not used to having motionless day sleeps, he will jolt at the partial awakening times (every 10 minutes of sleep) You can place your hands on his limbs to help him resettle. (there's a post in the newborns thread about partial awakenings and jolts)
It will take time, typically it takes 3 weeks for the circadian system to reset and new habits become completely adopted. So be patient, consistent and stick with the new routine. At first, it will be a challenge, but it will improve over time.
Hope this helps!