I personally don’t know about this concept “datoparkering”. I do, however, not frequent the larger cities that much so maybe I am just unenlightened.
Searching for it seems to reveal some evidence that it has at least historical truth. There is a very short WP article (https://da.wikipedia.org/wiki/Datoparkering) which gives no references. However, searching in historical dictionaries yields a result (https://ordnet.dk/ods/ordbog?query=datoparkering) which quotes the Danish newspaper Politiken from 1939-06-09 for saying something like; “not a single car knows about date parking, as the municipality is keeping it a secret”. And also quotes an encyclopedia “Nordisk Konversationsleksion” from 1945 for saying; “date parking has been introduced in Copenhagen for temporary testing in the streets Farvergade, Kompagnistræde and Læderstræde”.
Both these agree about the condition being that parking is allowed on the side of the road where the day and house number oddity matches (parking allowed on the even side on even dates). This seems indeed to be opposite of Sweden where the Wikipedia article says parking is prohibited when they match.
The current official legislation “Færdselsloven” (https://www.retsinformation.dk/eli/lta/2017/1632) however, does not include explicit signage displaying or mentioning in writing anything about date (“dato”) or parking. I think, however, that such restrictions could be imposed by the general parking prohibited sign “C 62 Parkering forbudt” with the sub-sign “U 33” specifying further conditions. U 33 example says “1 hour” but wording doesn’t prevent other restrictions not mandated by a period, it explicitly mentions that it could be conditioned to only be valid “on certain weekdays” (“på visse ugedage”) and “certain slots of time” (“inden for visse klokkeslæt”).