Coming along a little late to the discussion but your DS sounds IDENTICAL to mine! (my DS has just turned 7, is very sensitive & quiet yet popular and enjoys joining in and being 'part of the gang'. He also is completely rubbish at entertaining himself - his 2 sisters can play for hours on their own, he just moons around saying "i'm bored, can I watch tv?".I swear its a boy / first born thing, but thats an entirely other thread!).
Only now is he starting to do after school activities - a footy club that runs on the school field straight after school. Swimming on a sat morning (that he would give up instantly if I let him, but I think swimming is important). He now also does a friday afternoon tennis club which he adores, but ONLY if he knows i'm in the clubhouse waiting for him or, better still, watching from the sidelines. He hates to be left.
This half term we signed him up for 2 days of football camp (10-3, so not full days), because he gets so bored in the holidays. Its run by the same guys who run his after school club, doing it on the school field and most probably with lots of his mates from school.
Yesterday was day 1 - he had a complete stressy meltdown monday night and declared he didnt want to go (he worries ALOT in advance about things). Stress again tues morning. I figured, whats the point in sending him to something that he is REALLY dreading (even though I KNOW he'll enjoy it whilst he's there), so we cancelled yesterday on the premise that he will go today. He did get up quite happily this morning and got dressed for footy and went to the camp (slight worries in car on way there). But i left him fine and he saw some mates and ran off across the field. Result!
But I do honestly know how frustrating it can be - on the one hand, you don't want kids to just give up at the drop of a hat, but on the other hand, I don't want to be sending my child to something they really don't enjoy. I know that my son is abit low in self esteem about stuff "i'm rubbish at football, i'm not the fastest runner, i'm not as clever as xx". IN fact, he's really pretty good at football, is probably top 5 out of the boys in his class for academics (based on what teacher tells me, not me nosying around classroom!), he just needs to believe in himself more.
Anyway, this is rather alot of waffle and not alot of help - just really that you're not alone. I think there are lots of quiet, sensitive boys out there who need little, gentle pushes in the right direction in order to achieve stuff they don't think or realise they can do alone. The right after school activities should (I believe) help these sensitive little chaps.
Hang on in there - we resolved the ipad issue by buying some decent educational games - squeebles spellings is ace (he loves playing it, PLUS he learns his spellings). He can play a more fun ipad game so long as he does 15mins of spellings first. We do limit screen time otherwise he would just sit on the sofa all day long.
Right, i'll sign off before I write an entire essay!!