you can also say dikensiz gül yoktur and it has more or less has the same meaning as dikensiz gül olmaz. (masters would help you with the slight differences if there is any)
var(dır) x yok(tur)
olur x olmaz
But you can read or hear a sentence in which vardır and olmaz can be used as antonyms:
dikensiz gül vardır, niye olmasın ki.
But in most cases var-olur / yok-olmaz are not interchangable.
sokakta bir araba var (you cannot say sokakta bir araba olur)
olur often doesn´t indicate possession
param var/yok
but in conditional sentences olur/olmaz may indicate possession:
param varsa / param olursa
The difference between the examples is that varsa indicates "the pesent time" and olursa indicates "the future time" (if someone says otherwise, fallow them not me)
paran varsa al (now)
paran olursa al (future)
olursa also means if happens:
öyle olursa (=if it happen like that) you can´t say öyle varsa instead of öyle olursa.
...
I think our official teachers would help you more... (but I see tunci is lazy today! )
(note for my dear friend nevbahar, "alışmış kudurmuştan beterdir" 
Great explanation once again by Master Scalpel [ Usta ağlatıyorsun ortalığı resmen !]
Evet, I am lazy nowadays...Btw I am looking forward Nev´s reply to your comment for her 
!!
Hadi Nev yüzümü kara çıkarma !
