A felony conviction does not automatically end the conversation, but it does mean the standard approval process will not work for you. The background check that every visitor goes through flags felony records, and a standard application will come back denied.
The path that exists for your situation runs through the warden's office. A special visitation waiver can be requested, and wardens do grant them in circumstances where the applicant makes a compelling case. A 2014 conviction with completed probation and a clean record since then is actually a reasonably strong set of facts to bring to that request. You are not a current offender, you are not on supervision, and a meaningful amount of time has passed since the conviction.
The approach matters as much as the facts. Write a formal letter to the warden that is respectful, humble, and forward-looking. Do not dwell on the conviction or make excuses for it. Focus instead on your relationship with your boyfriend, why maintaining that connection matters, and how your life has been conducted since completing your sentence. The goal is to give the warden a reason to exercise discretion in your favor.
The odds are genuinely about 50/50 on these requests. Some wardens are more accommodating than others, and the nature of both your conviction and your boyfriend's offense can factor into the decision. There is no guarantee, but it is absolutely worth the attempt.
In the meantime, letters and photos through InmateAid keep the connection strong while you pursue the waiver. That communication does not require any approval process and reaches him reliably regardless of the visitation situation.