JSON schema – valid if object does *not* contain a particular property

What you want to do can be achieved using the not keyword. If the not schema validates, the parent schema will not validate.

{
    "type": "object",
    "properties": {
        "x": { "type": "integer" }
    },
    "required": [ "x" ],
    "not": { "required": [ "z" ] }
}