In the common case where you trust your input entirely you can just interpret your string as JavaScript. Then you don't even need to use quotes for the key names.

    $ alias fooson="node --eval \"console.log(JSON.stringify(eval('(' + process.argv[1] + ')')))\""
    $ fooson "{time: $(date +%s), dir: '$HOME'}"
    {"time":1457195712,"dir":"/Users/jpm"}

It may be a bit nicer to place that JavaScript in your path as a node script instead of using an alias.

    #!/usr/bin/env node
    console.log(JSON.stringify(eval('(' + process.argv[2] + ')')))

Since fooson's argument is being interpreted as JavaScript, you can access your environment through process.env. But you could make a slightly easier syntax in various ways. Like with this script:

    #!/usr/bin/env node
    for(const [k, v] of Object.entries(process.env)) {
        if (!global.hasOwnProperty(k)) {
            global[k] = v;
        }
    }
    console.log(JSON.stringify(eval('(' + process.argv[2] + ')')))

Now environmental variables can be access as if they were JS variables. This can let you handle strings with annoying quoting.

    $ export BAR="\"'''\"\""
    $ fooson '{bar: BAR}'
    {"bar": "\"'''\"\""}

If you wanted to do this without trusting your input so much, a JSON dialect where you can use single-quoted strings would get you pretty far.

    $ fooson "{'time': $(date +%s), 'dir': '$HOME'}"
    {"time":1457195712,"dir":"/Users/jpm"}

If you taught the utility to expand env variables itself you'd be able to handle strings with mixed quoting as well.

    $ export BAR="\"'''\"\""
    $ fooson '{"bar": "$BAR"}'
    {"bar": "\"'''\"\""}

You'd only need small modifications to a JSON parser to make this work.