Couple is one of a couple hundred words in the English language that is categorized as collective nouns -- team is another very familiar collective noun, as are family and congregation. While it is evident these nouns describe a group -- more than one -- they do not always call for a plural verb.
With collective nouns, subject/verb agreement is determined by the manner in which the group achieves the action described by the verb: individually or collectively.
If it achieves the action collectively (as a single unit), your verb is singular:
- The couple is awaiting arrival of its first born;
- The team is in contention for first place;
- The family is picnicking at Lake Luster;
- The congregation has exceeded 350 members.
If it achieves the action by acting as individuals, your verb is plural:
- The couple are working at opposite ends of the city;
- The team are home with their families during the schedule hiatus;
- The family are avid cyclists;
- The congregation have diverse opinions on this particular church position.
In your specific example, we could assume that person one gave the guy slow-working poison on day one and person two shot him the next day. In the more likely alternative, we could assume the two people jointly beat the guy to death, and yet another song title is written in sloppy English :-)