WAPF says boil them for 3 1/2 minutes and that they should be soft and warm, not hot. I would think that would make them a little firmer, not runny but not totally cooked through. (discard whites if child is under a year)
I usually just throw the yolk in some butter in a pan and gently cook it for a minute or two. I'd probably feel better letting them be a bit more runny if they were from a local farm, but I am only able to get grocery store eggs at the moment. Anyway, neither of my two that I've given them to seem to have any issues with eggs.