When DD had something specific to look forward to - something she really wanted to do - then that helped her get through the tough bits. If there is something he could really concentrate on, it is likely to be successful, and kids there are likely to be like him, then its kind of like meditation for adults - just focusing on something gives them time to not be thinking the 'sad' thoughts IFSWIM.
I looked at kidscape - and others that I found doing a google search - all pretty helpful.
With judo - try and see if there is another child starting at the same time, then they can be new together. Also the kids find it hard to remember the names of the moves - so if he had a book to help him learn them, that would help his confidence - ie he might not master all the moves straight away, but knowing the names would help him feel part of it really quickly. Enjoy spending evenings with him pinning you down on a rug to practice the immobilisations!
I also spent alot of time with DD doing things together - making things, chilling on the sofa - so when things felt too much, she knew she had time with me with my undivided attention to look forward to when she got home. Also let her plan activities for an evening - nothing major / expensive - eg she wanted to make popcorn and watch a certain film on the sofa - just giving her a bit of control. We also practised the kind of sports things they played in the playground, so she felt confident that she wouldn't make 'mistakes' and give the kid a reason to laugh / sneer at her. I found out they were taking toys into school - so we went shopping.....came back with a 'girl' and a 'boy' toy so she could play with either group. Turned out there were lots of little things that we could change to help her - I hope he lets you help him - sounds like you are doing a fantastic job if he is really opening up to you and his brother & GF.
Also wanting to die is wanting to escape the life you have, not wanting to be dead IYSWIM - (I have very close friends who have done / tried so I'm not trying to trivialise what your son said) - the key is to think that it is temporary and it won't always be this way even though it feels like that now - kind of like riding out a storm - all grey and horrible, but eventually a storm clears. Small specific actions help to lift it.
There is also a book on Amazon on how to depression proof your child - which is very good for teaching children how to have more positive thinking patterns.
I really hope this gets better for you both .......