Lets say someone attempting to calumny, by fabricating a a written document. Can I call this event as "Calumny attempt"?
Yes, you can, and it is grammatical and understandable. It is probably not idiomatic. In English, two nouns are often used together this way, with the first "modifying" the second. Examples include umbrella stand, baseball game, rape attempt, murder rap (which has at least two meanings), school book, etc. When a combination is used with enough frequency, it is considered a compound noun.
The standard usages I see are:
"attempt calumny" (calumny as a verb) "attempt at calumny" (calumny as a noun) "calumnious attempt" (calumny as an adjective, as noted by WS2 above)
To clarify, the last would be best used in phrases like "A calumnious attempt to secure the fortune" and not as an object itself. If you just mean "What he did was X.", I would use "What he did was an attempt at calumny" or "attempted calumny".