Hi J.,
Please do not be dismissive of the fact that there are bullies on the playground. These children need to be dealt with--schools must start taking this issue seriously. Bullying can certainly be wearing on those being bullied, so just because he's been "fine" in the past does not mean he's not having issues now with it.
I grew up Roman Catholic. You said he just had his First Communion, so I wonder if he also had his First Confession? My First Confession was NOT a good experience at all, yes, it scarred me for life and I did not feel like I could talk to anyone at the time. Delve a little deeper into how he felt about making his First Communion and First Confession. It is also possible he gets sad in church because he is praying about some troublesome issues. I would recommend talking him to a counselor outside of and not affiliated with his school, so he can talk freely. It can't hurt.
I have an official diagnosis of Generalized Anxiety Disorder, so I can tell you the drug-free ways I cope with the physical symptoms. As with any disease, diet, exercise, and sleep are key. With anxiety, enough can not be said about getting solid sleep. Many people who are anxious can't sleep at night, and then become more and more anxious due to the lack of sleep. It is a vicious cycle!
I've found massage to be very helpful in keeping me relaxed. Find a good pediatric massage therapist, a male one if he wants. A good therapist will give him the option of being clothed if he is more comfortable, and even having you stay in the room.
I've gotten away from it, but in the past yoga was very helpful to me. There are lots of "kid" yoga classes out there. I also try to meditate at least once a week. There are lots of "ways" to meditate--some have religious aspects and others do not. It is basically about emptying your mind and concentrating on your breath. Aromatherapy is also helpful to me. I put a few drops of peppermint essential oil on a cotton ball and wipe it on my forehead, temples, and back of my neck. Peppermint, spearmint, and chamomile teas are very calming, especially before bed. Let me know if you want more info or need more resources. Good luck.