A couple is/are strolling in the Park.

A couple is strolling in the park.

A couple of people are strolling in the park.

If you are British, I think you would say "A couple ARE strolling in the park.

Depends where.

The English spoken in London is not the same as that spoken in Bristol, York, Newcastle, Cardiff, Edinburgh or Glasgow.

Having said that either term would be acceptable.

Be wary of Hightor's answers.

He seems to be of the impression that American English is the only form of English spoken, and as such claims to know more about how I speak than I do.