For more on genitive of time in English, I just found this in The New Fowler's Modern English Usage: 

The chiefly AmE type he works nights; she plays cards Thursdays is a concise way of expressing the general English type of an evening, of a Sunday afternoon, though this latter type, which is still current, is now beginning to sound literary or archaic. A typical example: All the intellect of the place assembled of an evening―Carlyle, 1831. Until the 19c. the type of nights, of mornings was also possible: e.g. Dice can be played of mornings as well as after dinner―Thackeray, 1849. 

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http://alexandriaesl.pbworks.com/f/The+New+Fowler%27s+Modern+English+Usage.pdf

I think this might be what I call "the genitive of indefinite time", similar to "jednoga dana" which means "one day" (ou bien, "un jour") in the sense of "one day, I'm not sure when." In German it's also in the genitive "eines Tages" and they also have other indefinite genitives "tages" "nachts" or, for example Heine, "Wenn ich an deinem Hause Des Morgens vorübergeh". It's a neat archaic Britishism in English as well to say "of a Sunday" meaning "most Sundays" <a href="https://www.macmillandictionary.com/us/dictionary/british/of-a-weekend-sunday-etc">https://www.macmillandictionary.com/us/dictionary/british/of-a-weekend-sunday-etc</a>;

There's a good overview of the genitives for time expressions in English, Old English, and German in 

Hvala puno na odgovoru, Milena i Kamenko!

I would definitely be interested in the different uses of the genitive case, I sometimes find myself scratching my head, wondering when exactly it should be used. I know it indicates possession, but other than that I only have hunches as to when to use it. Any help or direction would obviously be greatly appreciated!

Dear René, 

In your phrase "ovih dana" you should use co coled "Vremenski /temporalni genitiv" which indicates the time of the action. Ex.: Ona radi svakoga dana. Padala je kiš tokom cijeloga dana...It is only one of the nine modes of sage the genitive. (Deoni, ablativni, kvalitativni, subjekatski, objekatski, genitiv čudjenja, prisvojni, genitiv uz "eno, eto  i evo", vremenski ...). The usage of the genitive is very complex in our language. If you want, I could give you same more explanation. The other "problem" is the usage of the genitive with the prepositions. It is an other nightmare of our grammar. (Genitiv mesta, vremena, načina, uzroka, cilja, pripadanja, porekla). If you need more help, just give me a hint!

Regards!

U nominativu recenica jednostavno ne bi imala smisla. Glasila bi 'ovi dani, setam na posao'. 

Tacna ti je pretpostavka, tijekom ovih dana -> tijekom koga, cega -> genitiv