Can I come in?
A request to enter a particular place. A: "Hey, can I come in? I need to talk to you about something." B: "Sure, just close the door to my office."
Could I come in?
Do you mind if I enter? (A polite request. Also used with can or may in place of could.) Tom (standing in the doorway): Hello, I'm with the Internal Revenue Service. Could I come in? Bill: Hi, Tom. What are you doing here? Tom: Could I come in? I have to talk to you. Bill: Sure. Come on in.