I started a relationship with a coworker about 2 months ago. I'm a regular employee and he's the accountan analyst of the company. Recently I was called by the president and the director of operations for a management meeting. They informed me that since our relationship has become the subject of discussion among our fellow coworkers and it has affected the morale of the team I must either resign or end the relationship. They also state that the company is very small and they cannot transfer me.

The employee manual only states this: "Should two employees who work together or supervise each other enter into a personal, non-work related relationship, one or both employees may have to be transferred."

The thing is I was actually transferred from one department to another, and he does not supervises me in any way.
They say I must decide since I'm the newest member and not him.
I have one week to make my "decision"

What can I do?

Make the decision.

At-Will Employment (http://www.ncsl.org/programs/employ/At-Will-Employment.htm)

http://employeeissues.com/at_will_employment.htm

If you were transferred the subject should be closed isn't it?

Do you have a work contract ? You can chose to do either no neither.
If you tell them no, it will be up to them to make the next choice.