Theme option for card background image?

the card_mod is for the dark_sky custom card (note the syntax has changed a bit, add card_mod: :

type: custom:dark-sky-weather-card
card_mod:
  style: |
    ha-card {
      background: url("/local/images/weather-background-{{states('sun.sun')}}.png");
      background-size: 100% 400px;
    }

and also works on a regular entities card:

    - type: entities
      card_mod:
        style: |
          ha-card {
            background: url("/local/images/weather-background-{{states('sun.sun')}}.png");
            background-size: 100% 400px;
          }

      entities:
        - entity: input_number.test_level_1
          name: Level
        - entity: sensor.test_sensor_battery
          name: Level
        - type: section
        - entity: input_number.battery_level_critical
          name: Critical
        - entity: input_number.battery_level_warning
          name: Warning
      state_color: true

sorry you asked for button-card: wrong thread, go here :wink: and button-card uses different, Javascript, templates, not Jinja.