If I'm wrong, please someone chime in and correct me. As far as I know there is no Tracfone, Net10, or Straight Talk phone that you can keep the user from accessing the internet permanently. On a model or two I had in the past the most you could do was turn the internet connection off so you wouldn't accidentally use it but you couldn't lock it to 'Off' with a PIN or password so it would be easy to turn right back on. Any kid will figure out how to turn it back on in the first 5 minutes or sooner. For what you're asking you probably need to go to an actual cell phone carrier like Verizon, AT&T, etc... that would have that as an option or setting accessible through some account on their web site. Tracfone can't disable those settings on the carriers that they use, heck they can't do anything besides connect your phone to the carriers they contract to use (they don't own anything so they control nothing that isn't on the cell phone).
Now on the other side of the argument for Tracfone/Net10, you could buy him the coolest looking phone they have and make him buy his own minutes or only buy him a few each month, 30 or 60. After surfing on the internet with these phones he'd eat up all his minutes real quick, have none left, for a really crappy web surfing experience and realize it ain't worth it! Just don't buy him the unlimited plan on Net10 and it might work. Just my opinion.