I don't think the drive bay has room for more than the one 3 1/2" drive that is in there now (and the optical drive). However, most SSDs are small (2 1/2") and easily velcro'ed to any location there's room... if you want to go that route. But check that your motherboard has a free SATA port for the SSD's data cable and your PSU has an unused SATA power connector.
As an alternative, you may want to consider replacing your current HDD with a hybrid drive.
http://www.newegg.com/Product/Product.aspx?Item=N82E16822178381
You can get more details about it here: http://www.seagate.com/internal-hard-drives/solid-state-hybrid/desktop-solid-state-hybrid-drive/?sku=ST1000DX001