I've only read some of the posts in this topic, so excuse me if I mention something that's already been covered, or say something completely stupid, but ....
I've had a look at a map, while I agree in general that such a re-opening in basically unviable and therefore extremely unlikely, I think I have spotted a route that is possibly a bit more viable. It does however feature a big diversion from the direct route, and because of the nature of the terrain, will be very twisty and hilly in places.
From Carmarthen, the first 'major' station would be at Newcastle Emlyn before heading of to Lampeter (possibly via Landysul). After that, it will be another big turn in the route to Aberaeron before running along the coast upto Aberystwyth. To save some money, instead of building stations at every village along the route, space could be cleared and reserved for possible stations in the future, with the main towns along the route becoming local/regional hubs. This (IMO) is quite possibly the best route available, the big down side is the very twisty and hilly nature of the route due to the local topography.
That sounds as though it would be a lot more expensive than reopening the old line, but with only a little more demand created by going through the small towns in the area. I think that the benefit of serving these places may well be mitigated by the time penalties in any case, sorry.
My father often talks fondly of taking the train from Cardiff to Aberystwyth when he was a student in the 1950s! He certainly regrets the closure of this route. I'd love to see it open again but appreciate the business case isn't very sound.
I'd love to see it open again too, but to say that the business case isn't very sound (by the way these things are currently assessed) is a massive understatement!
As a purely hypothetical alternative, how about reconnecting the Heart of Wales and Mid Wales lines, to give some access from Aber to the South Wales coast?
The ever-useful Adlestrop atlas shows a line running from Builth Road to Moat Lane Junction, via Rhyader and Llanidloes. It doesn't look like a fast option but surely some reconnection of the Mid Wales railways might help?
http://www.geowiki.com/New_Adlestrop_Railway_Atlas.pdf
That's a more reasonable suggestion, but still pretty optimistic. The difficulty in utilising the HoW line now is that it's quicker to travel to Shrewsbury via Cardiff from anywhere east of Llanelli. Given that the Mid wales route was pretty slow due to the terrain, I'm not at all sure that the time saving for a traveller from or to Cardiff would be significant via Builth Road.
As I've commented already, the market for travel between Cardiff and the Aberystwyth area doesn't seem to be particularly large, it';s more of a niche market with the addition of some student traffic at certain times which is probably best catered for by coach.