"The forks are yours."
You actually could but you have to use the plural marking. So it has to be Çatallar seninkiler.
Yet there is a little difference in meaning. Compare
Çatallar senin. - The forks are yours. (The forks belong to you.)
Çatallar seninkiler. - The forks are yours. (The forks are your forks. or The forks are the ones belonging to you.)
So we use seninki only as a pronoun in order to avoid repeating the same word. Not as an implication of possession.
Benim arabam mavi. Seninki (senin araban) hangi renk? - My car is blue. Which color is yours (your car)?
Bu araba benim. (bana ait). -> This car is mine (belongs to me).
Bu araba benimki (benim arabam). -> This car is mine (my car).