Fred,
Others in the forum may be able to provide you with a precise answer to your question. But for as long as I’ve been around Sunbeams, I’ve always understood the body dimensions for a 66 Alpine and Tiger to be the same, especially around the cockpit. Therefore, I would think that your tonneau cover should fit. I would hasten to add, though, that 30 year-old vinyl material may have lost it’s ability to “stretch-to-fit” and thus be the source of your problem. I encountered the same problem after I restored my Tiger. No amount of Amour-all or vinyl cream would bring the suppleness back. Getting a new replacement in on my wish list for next driving season.
Congratulations on your return to Sunbeams and best of luck!