Having taken private voice lessons for the past two years, I would recommend this... Ask around, and see if there are any particular names of teachers that seem to keep popping up. See if anyone you know has had voice lessons before, and see what they have to say about their teacher. When you do find someone, a good way to see if they'll be someone that you can trust, is to talk to them on the phone, and arrange a meeting with the teacher before hand. A good teacher will likely want to talk to both you and your son, as well as hear your son sing, or at least talk to him about why he wants to sing. After this meeting, it is I'd recommend asking your son if he liked the man or woman, because vocal singing involves a great deal of trust between student and teacher. This is because singing requires one to use their body as their instrument, and your son would have to be comfortable enough with the teacher to say, be okay with them teaching him how to breathe efficently, or how to loosen up his neck and shoulders so that the tone is not strained by tension.
Finally, I do want to warn you, that because your son is only eight years old, many vocal teachers might recommend that he not start private vocal training right away, but instead start out with a children's chorus. That way he'd get experience with reading music, and sight reading, and wouldn't burn himself out or strain his voice. Then, if he still likes singing as much as he does now, when he's say, 13 or 14, his voice will be almost ready to change, and he'll have a great deal more knowledge of how his throat feels. This way, when he takes the step to private lessons (and it can be a rather large step) he'll know his capabilities and limits, and will be able to know when he needs to take a break and get a glass of water, or when he can keep singing for another twenty minutes etc...
Anyway, I hope this helps, and I wish you and your son the best of luck.