A PCIe to PCI riser card doesn't really exist to do what you want. I've seen PCI to PCI-E x1 adapters, however these require modifying to work with graphics cards as they are typically PCI-E X16, and thus larger than an X1 slot. I wouldn't recommend going down this route as additionally, the PCI interface will choke any semi modern graphics card due to its low bandwidth and outdated design.
The issue I see, is that it sounds like you have an oddball case if you need a riser card, so will a newer motherboard fit? And, if your board is old enough to have no PCI-E slots, is the rest of your system up to spec to make a new graphics card worthwhile at all?
If you could give us a little more information about your computer, we can see what would be the best option for you.