"Plural" is to "pluralize" as "possessive" is to...?

Oh, certainly, possessivize is a perfectly cromulent word.

It's just not used very often because people don't discuss grammar seriously very often (I often claim that grammar is the last taboo subject in America — bring up a grammatical topic next time you're at a cocktail party and watch what happens).

But I assure you that any linguist could rip off a possessivize or two without batting an ear — when talking, for instance, about vowel changes in genitive case forms

"When you possessivize vowel-stem animate nouns you get fronted vowels before the /-ki/ genitive, but not before the /-qi/ genitive."

It's just a technical term, is all.

It depends what you're looking for in a word.

• Do you simply want to communicate your meaning?
• Or do you also want to do so without a significant proportion of your readers sitting up and saying "hey, that's a made-up word"?

If you're looking for the latter, I don't believe there is such a word. You have to use the phrase "to make possessive".

How do you pluralise chicken?

Chickens

How do you make chicken possessive?

Chicken's

Alternatively, keep using the word "possessivise" or "possessivize" (as many people are already doing). Everyone will know what you mean. It will jar for them, as described above, the first dozen times or so they see it. Do it enough, and encourage enough people to do likewise, and it'll be a dictionary word within 10 years.

Remember, there was a time when blog wasn't a word.