This question belongs in the armor and props subforum.
I'm not an expert on armor, however I know you'll probably be forking out a sizable amount of money for a better quality costume. Most children's costumes are cheaply made Halloween costumes, not higher-end cosplay costumes. You'll most likely have to get it commissioned (which you can ask about in the commissions subforum) from somebody.
FYI, commissions are *not* cheap. You're paying for supplies, (and higher-quality armor supplies like worbla and wonderflex are pretty pricey) as well as the custom design process, pattern drafting, armor shaping, sanding, priming/painting, the time involved, and the person's skill/knowledge.
Commissioners usually make costumes for teens/adults instead of children, so don't be surprised if they charge you extra for making a custom size they're not used to making. And if you want it done by Halloween, you may have to pay a rush fee to get your son's costume bumped to the top of the commissioner's queue, (especially since this is a busy time of year for cosplay commissioners) as well as pay for faster shipping.
I highly doubt you'll find anyone willing to make it for under $250-300 at the lowest. If you want to do it any cheaper than that, I'd look up storm trooper armor tutorials or settle for the Halloween store costume.
Currently working on:
Moon Moxxi: Borderlands Pre-Sequel
Saul Goodman: Breaking Bad
Benny Gecko: Fallout: New Vegas
Momoko Koigakubo: Ghost Stories (Dub)
Cameron Van Buren -- MPGiS
Malory Archer: Archer
Kamala Khan: Ms. Marvel
Vader Eloha/The Queen: OFF
Princess Suwa: Mascot of the city of Suwa, Japan