Org babel "Supported languages" are languages that you can evaluate/execute directly from an orgmode code block. I don't think JSON and XML are executable languages anywhere, so you don't need special support for them. You can still use src blocks, and if there's an Emacs mode for editing the language, it will apply the formatting to the code.
If you have JSON mode installed, you could use that. I don't, but JSON is close enough to Javascript that it produces reasonable formatting:
#+begin_src js
{
"firstName": "John",
"lastName": "Smith",
"isAlive": true,
"age": 27,
"phoneNumbers": [
{
"type": "home",
"number": "212 555-1234"
},
{
"type": "office",
"number": "646 555-4567"
}
],
"children": [],
"spouse": null
}
#+end_src
Which appears like this:
xml files are edited in the built-in mode nxml
by default, so you don't need to add anything to use it:
#+begin_src xml
<note>
<to>Tove</to>
<from>Jani</from>
<heading>Reminder</heading>
<body>Don't forget me this weekend!</body>
</note>
#+end_src
Which is formatted as: