Here is an example of how to pass in the custom property object:

{
  ...
  "CustomProperties": [
    {
      "PropertyNumber": 1,
      "StringValue": "new string" // used for strings and as the default type
    },
    {
      "PropertyNumber": 2,
      "IntegerValue": 3 // used for integer and number fields, as well as list and user fields
    },
    {
      "PropertyNumber": 3,
      "DateTimeValue": "Thu Oct 31 2019 10:28:11 GMT-0400 (Eastern Daylight Time)" // used for date time fields. Use a standard JSON date object for v6 of the API
    },
    {
      "PropertyNumber": 4,
      "IntegerListValue": [1,2,3] // used for multi select lists
    },
    {
      "PropertyNumber": 4,
      "BooleanValue": false // for boolean fields
    }
  ],
  ...
}