Hi,
Generally the genitive case of a noun is used to show possession. For example, "the family's dog" is "canis familiae" (the dog of the family). But there's other ways too. There's the good old possessive adjective: "my dog" is "canis meus" (where meus is just an adjective describing the dog). You can use a specific adjective if one exists: "the family's dog" can also be "canis familiaris" where familiaris is an adjective meaning "belonging to a household / friendly, intimate."
So there's not just one answer. Generally it's a good idea to take the formula:
Blah blah XYZ, which is property of ABC, blah blah.
Find the noun ABC in latin, find its genitive form (which is different based on the noun and its declension), and change to:
Latinblah latinblah XYZ ABCgen latinblah latinblah.
Because this will be the XYZ "of the" ABC.
Or I guess you could just do a literal translation (still requiring the genitive of family):
canis possessio familiae est.
Hope this helps