Have you tried taking him swimming? Isla started swimming at 4 months and she absolutely loves it, plus it really tires her out so she sleeps better after swimming. It is my go-to activity when I am exhausted trying to entertain her because it pretty much perfectly fills the two hour time between naps by the time we drive there (30 min away), get changed, swim for 30 min, get showered/changed, and then drive home. By the time we get back she is ready for a nap and I didn't have to think of a million activities to fill the time between naps.
Isla has been teething since about 4.5 months old (and still no teeth!) and being outside seemed to be the most distracting thing for her. So we would go out on a blanket in the yard with her toys, or a picnic by the river, or a walk/jog in the stroller, or I'd put her in the ergo or hiking pack and take the dog for a walk/hike. I had teething rings/toys attached to the stroller/ergo/hiking pack so she could chew on them while we were out and about. In the house we had "stations" set up, the jolly jumper, tummy time, bumbo, etc and when she would get bored or fussy I would move her to the next "station" where she would be entertained for a while and I would just keep rotating her around. She is not a cuddly baby so it would be very difficult because she would be whiney and want me to pick her up/hold her, but as soon as I was holding her she would be squirming and trying to get at something to play with, but then when I would put her down so she could play with whatever she was trying to get at she would fuss again.
I would also try to run errands with her like getting groceries or whatever, so I wasn't just stuck in the house listening to her whine. And it helped her to be in a new environment rather than in the house playing with the same old toys. Or if we were stuck in the house I would put her in the ergo and clean or cook.
I found teething much easier to deal with once she was eating finger foods because it was both entertaining for her to try new foods, and also soothing on her gums to chew on raw peppers and cucumber sticks. Do you have any of those teething rings that go in the freezer? Isla gets a lot of relief from those. Teething can go on for a long time, but at least for Isla she seems to have gotten used to the feeling and gets less and less fussy and upset with each bought of teething she goes through. Now if she would only just get some teeth already!
