This page contains all the information you need on how to have a romance with Diana Allers.
Before you can even consider Diana as a romance, you’ll need to welcome her to the Normandy by speaking with her at the Citadel Dock: Bay D24 after completing the mission, Priority: Mars. She’ll ask you if she can join the Normandy to create news and you’ll want to say “Let’s do a trial run”. Now Speak with her in the Starboard Cargo Room to progress your relationship with her.
Once you’ve completed Priority: Citadel, speak with Diana and then go up to your cabin to continue the interview. After the interview has come to a close, say “I’m okay with that” to progress the romance.