We all sympathise with you as it's very wearing, having a baby cry a lot. First of all, I expect that you've checked that he's not in acute pain eg earache.
Some babies who are constantly crying benefit from treatment from an osteopath - cranial osteopathy, very gentle and not at all painful. This needs to be done only by a qualified person. My friend's daughter is an osteopath and has had great success in treating crying babies. It realigns the bones in the skull which can sometimes cause babies to be in pain.
Does he switch off crying when you pay attention to him?
He might be bored if he can't sleep. Try putting on some quiet, soothing music near him - not pop. Mozart has often been successful in soothing crying babies. Perhaps you could record your voice, speaking or singing, and leave it playing nearby.
When my oldest grandson was a baby, and we were baby-sitting, he was an s*d to get off to sleep, and I used to sing to him - probably bored him silly!
Has he got something to look at eg a mobile? Until babies are big enough to sit up, they often get bored, so something colourful and active can help to occupy them. Perhaps he could be with you in the kitchen, lying in his baby chair, as often, all they want to do is see you and feel secure. Don't carry him round all the time - it'll only hurt your back and he needs to get used to the fact that sometimes he can just to be close to you, but not picked up. Talk to the baby while you are giving your other child his Mummy time. He'll get used to it if you have the energy to cope with it.
I know this is a bit dodgy with a boy, but when my daughter was about that age, we used to take her nappy off, putting an absorbent wad/towel under her in the pram, so that she could kick her legs freely, and that usually gave us time to eat our meal.
When he's a bit older, he could go into a baby bouncer for