Κύριος means Mr. or Lord. So κυριακός is "belonging to the Lord".
I don't think 'κυριακός' exists as an adjective... You just say 'του κυρίου'/'της κυρίας'. Κυριακή is as you explain the day of the Lord, like 'domenica' is.
There is something very odd with κυριακός My dictionary Babiniótis does not give κυριακός at all, it only gives the adj. κυριακάτικος. But in the ethymology it says:
Κυριακή a substantivation of the ADJECTIVE κυριακός, and
κύριος/ mister, sir, lord - ancient κύρος - I.E. keu- (to swell/ expand), also cumulus and cumulate come from this as well as the Gr. wave = κύμα
Babiniótis also gives Pater Noster/ Pάτερ Ημών as Κυριακή προσευχή , prayer of Sunday, where κυριακή is an adjective;;;???
It was an adjective in Ancient Greek, but it's really "underused" in Modern Greek, and actually used in "fossile" phrases such as Κυριακή προσευχή (unless you write a poem or something!). Κυριακάτικος is the "related to Sunday", not "related to Lord". There is also the name Κυριάκος/Κυριακή which is actually that adjective as a name.