No experience with this with my own daughter, as she was the one howling at the injustice of the minimum heights at roller coasters many adults wouldn't touch.
However, I did get to experience this once with my niece one afternoon, and she was also around 10 at that time. She asked me to go on the (rather tame) roller coaster with her but told me how scared she was. We waited through the line for a while before she was ready to abandon, so we did. We went on to enjoying the park for a little while, and she brought it up again. We got back in line again, and this time she made it through.
I did encourage her to face her fear and told her there was nothing to worry about, and the ride was a lot of fun (and to a kid who never rode a real roller coaster, it probably would be). I stayed in line with her until she hit her breaking point, and then I left with her without putting any pressure on her. We went on other things without me ever bringing it up again. She broached it when she was ready, but started making bargains with me - could she hold onto me the whole ride? I was agreeable to whatever terms she wanted.
The big things that worked here:
- Child led
- No pressure
- Comforting
And this is probably a factor, though my niece didn't explicitly say so - my fearless daughter five years younger than her had already ridden this thing several times that day. Is your 6yo riding the rides that DS10 is abandoning?
The major source of frustration in dealing with this sort of thing is the length of the lines, so I'd do whatever I could to mitigate that as a factor to help him work through this. That might be some combination of smaller parks/fairs, off-peak hours, or paying extra for passes that help you avoid waiting in line. The episode for my niece happened at a smaller park.
