safeStringify.js

const UNSAFE_CHARS_REGEXP = /[<>\/\u2028\u2029]/g
const ESCAPED_CHARS = {
    '<'     : '\\u003C',
    '>'     : '\\u003E',
    '/'     : '\\u002F',
    '\u2028': '\\u2028',
    '\u2029': '\\u2029'
}
function escapeUnsafeChars(unsafeChar) {
    return ESCAPED_CHARS[unsafeChar]
}
function safeStringify(input) {
	const rawString = JSON.stringify(input)
	return rawString.replace(UNSAFE_CHARS_REGEXP, escapeUnsafeChars)
}

usage.js

var input = { a: "<script>alert(123)</script>" }
var output = safeStringify({ "a": "<script>alert(123)</script>" })
console.log(output)
// => {"a":"\u003Cscript\u003Ealert(123)\u003C\u002Fscript\u003E"}"
var roundtrip = JSON.parse(output)
console.log(roundtrip.a == input.a)
//  => true