If it's not a wheel it's got to be a ball joint or bush. Spray some WD40 or similar onto one bush/joint at a time and see when the noise stops.
Can't really help you anymore than that with hearing it.
I'm guessing its a bushing.
The owner of the ATV should try driving it on a very flat ROAD and then slowly drive it down a rough trail (go over logs, put the tires in holes etc)...
if it doesnt squeek on flat road, but it squeeks on a trail, its most likely a bushing. I'm not familar with HOnda bushings, but if the ATV is more than a few years old the bushing probably needs replacing. If this is the case, I'd do all bushings at the same time. I find they tend to wear out about the same time
WD-40 is the worst of all spray lubes!!!! I can't get my head around how it's so popular with all the other options out there