PLEASE READ CAREFULLY, THERE ARE CHANGES YOU NEED TO MAKE!
I am sorry for the inconvenience, I think going forward we have much more stable position.

BREAKING CHANGE

1. You need to update the YAML configuration (or you can remove config from YAML completely and configure the sensors from Configuration/Integration page) - try it, it is cool I think.
2. The monthly_day_order_number option was renamed to weekday_order_number for better clarity. So if you use monthly frequency, you need to change the name of this parameter.
3. The implementation of permanent fix for #18 has two implications:
   a) Change of the entity_id is only possible if the sensor is configured from the Integration page. Previously, you could also change it if the sensor was configured in YAML - this is no longer possible. So if you need to change the entity_id (e.g. Japan), please migrate your config from YAML to Integration Page.
   b) As a leftovers from the 'quick fix' for #18, there might be orphaned entities in the Configuration/Entity Registry. They will be typically using the default entity_ids, so new entities will be created with _2 at the end. To fix that, you need to remove the entities manually (see bellow).

CONFIG CHANGE

Old

sensor:
  - platform: garbage_collection
    name: 'Waste'
    ....
  - platform: garbage_collection
    name: 'Another waste'
    ....

New

garbage_collection:
  sensors:
  - name: 'Waste'
    ....
  - name: 'Another waste'
    ....

RECOMMENDED UPDATE PROCEDURE

1. Update integration
2. Comment the integration configuration in YAML
3. Restart HA
4. Go to Configuration/Entity Registry and remove the Orphaned garbage_collection entities
5. Now you can either configure the sensors from Configuration/Integrations (hit the + button, select Garbage Collection and configure) - in such case, the sensors are added dynamically, no restart is required. Parameter changes are possible from the Integration page as well (the gear icon on top)
6. ...or, change the YAML configuration - restart Home Assistant.

NEW FATURES

1. Configuration is now possible from Configuration/Integrations using Config Flow wizard. The configuration through YAML is still supported as well.
2. Adding annual frequency for scheduling birthdays or similar annual events (Feature request #20)
3. Readme has been updated for better clarity.

Note: This has been major code re-factoring. Big thanks to @ludeeus for showing me the direction!