For what its worth I've just been though the process of choosing tyres for my 2012 Duratec Plus 4, after a huge amount of research and much deliberation I actually settled on a set of Continental Eco Contact 6 in 185/65-R15, and I've been super happy with these tyres from day one.
Some more detail here....
http://www.talkmorgan.com/ubbthreads.php/topics/757854/what-did-you-do-to-your-morgan-todayDon't dismiss going down to a 185 just because Morgan specified 195, a Duratec Plus 4 makes 143hp and only weighs 930kg so a 185 is more than enough tyre for the car, 185s will give you lighter steering and more feel too

Keep in mind even a small hatchback these days weights 1,200kg or more so modern tyres are typically made with far higher curb weight vehicles in mind, and as others have already said do make sure you dont buy a van tyre and they'll be made for even greater loads. For a tyre to work well on a far lighter vehicle like a Morgan, and assuming you want decent ride quality, you need something with a softer sidewall than you normally find on a modern tyre, the Continental Eco Contact 6 definitely ticks this box.
I purchased from my normal go-to tyre seller Camskill who are seldom beaten on price and offer excellent customer service, the guy there advised me that for a light car like the Morgan I should choose a tyre from a good manufacture's Eco range. This was a bit off-putting at first as I wasn't looking to save MPG and Eco doesn't sound very exciting now does it?
However, there's logic in the advice, apparently Eco tyres achieve the improved fuel economy partly by virtue of a softer sidewall, the happy accident being that this makes Eco tyres perfect for light cars. Don't be put off by the term Eco thinking such tyres arent suitable for enthusiastic driving, my Continental Eco Contact 6 grip brilliantly in both the dry and the wet, I drove Monty to Goodwood at weekend and the rain was truly biblical and I have to say my these tyres performed outstandingly well
http://www.talkmorgan.com/ubbthreads.php/topics/175520/1317/so-have-you-driven-your-morgan-today