You can either say Δίπλα σε εμένα -or- Δίπλα μου (weak form of the pronoun) ;)
Μου is the weak type of the personal object pronoun,two ways to say this,είσαι δίπλα μου or είσαι δίπλα σε εμένα (σ'εμένα)
Your own suggestions include near for διπλα, so how come you say it's wrong?
Because not all hints are correct in all contexts. Only the first hint is guaranteed to be correct. ;)
Δίπλα is "next to". Κοντά is "near". You can be near but not next to someone.