I was thinking building something of my own, but there is no easy API or anything that seems to be public.
I think you have to parse the website generated at each request to find the dates for each collection.
Any help would be much appreciated! :)

https://www.narabtomningskalender.se/
Search for e.g., my address: "Snyggatorpsvägen 1"

When incpecting the network traffic, this is the page being loaded:
https://www.narabtomningskalender.se/basfiler/online_kalender_skapa.php?hsG=Snyggatorpsv%C3%A4gen%201&hsO=KLIPPAN&knR=31811&abK=VILLOR&nrA=10012108007&lang=sv&clid=e97828682dc80c2b36df990778fb41a1

GET variables used in the query:

• hsG: Street name and number (yes, with spaces...)
• hsO: City
• knR: Customer number (as seen on the agreement/invoice, or just by searching for an address and inspect the traffic...)

It might also be nescessary to have a paremeter for the GET variable abK, which have at least the following options:

• VILLOR (e.g., your own house)
• FLERFAMILJ (e.g., apartment building)
• VERKSAMHET (e.g., company)

Although, probably VILLOR is the only necessary option as you don't care much when the collection in aparment buildings is.