Lisa that sure would be an ambitious project for a beginner to try and sew a fitted slip cover. There are things to be considered such as is it 2 or 3 seat cushions and back cushions - or is the back semi-attached, is it skirted?
Have you checked w/Bed Bath & Beyond or any places like that - they may have fitted slip covers for sleep sofas. Also, if your sofa is has "good bones" and is still in good condition except for the cover, it might be worth your while to invest in having it recovered.
Lisa I somehow managed to misread your question. I thought you were asking about a sleep sofa - don't know HOW I came to that conclusion - however, the info I gave you above still applies.
I have a question for you though - what is a "conversation sofa"? I've worked with furniture all my adult life - just not familiar w/that term.
I read your post and recalled seeing that exact project on this blog. She has a full tutorial: http://theinspiredroom.net/diy/how-to-make-a-couch-slipcover-honeybear-lane/
Lisa - I need to do the same thing to my conversation sofa. What did you find out?
Any place where you can buy replacement slip covers for your "curved" couch?...
I have made slipcovers for love seat and big arm chair, but I am an experienced seamstress. For a fitted cover measure plus 10" for tucking. Use an old sheet as a pattern. Sew tucks around curved places like the arms for a snug professional fit. Cushions with seperate casing and piping. If it does not require a skirt, allow enough for under the sofa and a drawstring casing. Good resources can be from your local library.