Mutate tag with json

As @basdebruin said, you need to create or retrieve an existing tag using the following mutation:

mutation {
  create_or_get_tag (tag_name: "my_tag") {
    id
  }
}

Then proceed with the regular mutation

mutation {
  change_column_value (board_id: 123, item_id: 456 column_id: "tags", value: "{\"tags\" : {\"tag_ids\" : [789,123]}}") {
    id
  }
}

Just to let you know that there are currently a couple of bugs when you assign tags to an item thru API:

  1. The new tag, if not already shown by another item, doesn’t appear. You need to refresh the page to see it;
  2. Tags created thru API don’t appear in the dropdown list.

Monday devs (@dipro) are already aware of the problem.