For example, how does one say the equivalent to "a day which made me content" or a "contenting" day?
The word you are looking for is most likely contentful, which although uncommon, is a delightful word. For example "it was a contentful day at the waterfront."
I'd go with "satisfying," "fulfilling" or "rewarding."
As in, "It was a satisfying/ fulfilling/ rewarding day."
Here is the list of synonyms for content from Oxford American Writer's Thesaurus.
Contented, satisfied, pleased, gratified, fulfilled, happy, cheerful, glad; unworried, untroubled, at ease, at peace, tranquil, serene.
You can't say contending day. Contending is an adjective and means competing.
The debate continued between the contending parties.