Raspberries are less fussy than lots of fruit about full sun and I've grown autumn fruiters in a semi shady bed successfully.
A large trough would be better than a pot as they send out lots of suckers which there wouldn't be room for in a pot. You'd only have room for one or two plants in a large trough though.

Also, as they are quite shallow rooted, you will need to give them a watering, if no rain, every week. They love a frequent, high potash feed, or even ericaceous feed. Rose feed is also good. In the ground I feed monthly, but in a trough/pot you may need less strength but more frequence. Especially once they start fruiting. Can you cut the bottom out of the troughs/pots and let them root into the ground? Autumn Bliss are my favourite raspberries. The main plant will be perrenial for about 5 years if fed properly. The suckers can be a pain and can be just pulled out or cut off. When your main plant stops producing so well, allow it to sucker, then transplant the sucker to a new pot/trough with fresh compost to start the process all over again. Cut down hard in late winter/early spring.

as a basic rule of thumb the bigger the pot the better the chance of sucsess excuse my spelling as avkq47 has basicly said .

Thank you to everyone who replied to my raspberry question! I shall try to take all your info into account when I get my mini fruit garden going. Jenko.

your more than welcome .