To update a custom deal field value, the following permissions are required.

Deal permission: the user should have permission to manage deals.
Pipeline-specific permission: the user should have permission to manage the pipeline that the deal belongs to. If the user does not have the permission to manage the pipeline, limited deal data are returned with only id, title, and isDisabled set to 1.
When updating a field value for a multivalued field (checkbox, multiselect), values must be strings in an array, e.g. ["Option 1", "Option 2", "Option 4"], whether one value or multiple are being set.

{
  "dealCustomFieldDatum": {
  	"fieldValue": "New title"
  }
}

{
  "dealCustomFieldDatum": {
  	"fieldValue": "option 1"
  }
}

{
  "dealCustomFieldDatum": {
  	"fieldValue": [
   	 "option 1",
   	 "option 3",
   	 "option 4"
  	]
  }
}

{
  "dealCustomFieldDatum": {
  	"fieldValue": 9999,
  	"fieldCurrency": "cad"
  }
}

{
  "dealCustomFieldDatum": {
  	"fieldValue": "100.99"
  }
}

{
  "dealCustomFieldDatum": {
  	"fieldValue": "2018-12-31 00:00:00"
  }
}

{
  "dealCustomFieldDatum" {
  	"fieldValue": "2020-05-19T02:45:00-05:00"
  }
}

{
  "dealCustomFieldDatum": {
  	"fieldValue": [
    	"option 1"
  	]
  }
}