Is Carnfunnock Country Park a sensible planned stop on the Causeway Coastal Route?

Yes.

Carnfunnock is on the Coast Road in the Ballygally–Larne stretch and has designated car parks, woodland, gardens and coastal viewpoints. It makes a more sensible scheduled break than pulling over on a narrow section of the A2. The published visitor information gives daily car park opening arrangements, but these can change and are separate from general public-road access. Use the signed entrance, enjoy the site on foot, and check the closing time before committing to a longer walk.