Dogs are a huge problem in non-pet friendly apartments. If you're apartment is carpeted forget about it, there's little to no chances of you being allowed to get a dog. You're also going to have to demonstrate that the pet is trained and you'd have someone available to take him out during the workday.
You can grease the super's palm but if the dog barks and a neighbor complains to the management company they'll come up with creative reasons to take the security deposit, illegal dogs =\= normal wear and tear