I´m sure there are SOPC ready IP´s in the SOPC Builder. So you can build your own NIOS CPU with a sd-card IP and then you can open it and handle it like a file.
this pdf shows you what you have to do to use the IP-Core succesfully. There are also examples. I think you can copy them.
I hope this will help you.
**broken link removed**
pls look at the example in SD/MMC SPI Cor