"This is mine."
it is more colloquial but still widely used. I also learned it as 私のです for it is mine.
Becaise kore always takes a particle wa/ga/ni etc. You can not put kore next to a noun so kore mono is wrong. Kono can not take any particles it can only be put with nouns like konomono
Like Hiba said, you must always put a particle after これ，それ，あれ and you must put a noun after この， その， あの。
I believe it is because the わたしの construction requires something after it, の implies ownership, so わたしのです wouldnt make sense as there's nothing being owned. So literally, これ は (this is) わたしのもの (my thing) です
I actually learned it as これは私のです. But I do not know if it is colloquial or not.
Ugh, such an old question and still it doesn't accept the right answer. Oh well, I'm very glad I didn't start earlier!
For duolingo, です is not optional. It is only accepted optional for い-adjectives.
But the answer is okay I guess? Why don't add it if it's okay? I reported, but the fact it didn't added before shows a lot.
The reason it's not accepted is because it's not the type of Japanese you should be in the habit of using. Very "slangy" and impolite. So since this is for beginners in Japanese, they will not be adding this as an accepted answer.
It is okay, but it is colloquial, it should be accepted as well as an alternative answer, leaving the more polite form as the main answer.