Sorry, but I have no recommendation... my computer is much newer and I have no experience with older Macs.
Here are the listed requirements for Parallels 8. You should be able to determine if your computer meets these specs.
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Parallels Desktop 8 for Mac Requirements
Hardware Requirements
* A Mac computer with an Intel Core 2 Duo, Core i3, Core i5, Core i7, or Xeon processor (Core Solo and Core Duo processors are no longer supported)
* Minimum 2 GB of memory (4 GB or more of memory is recommended to run Windows 7 in a virtual machine or if your host OS is Lion)
* About 700 MB of disk space on the boot volume (Macintosh HD) for Parallels Desktop installation
* About 15 GB of disk space for each virtual machine
Software Requirements
* Mac OS X Mountain Lion 10.8
* Mac OS X Lion 10.7.4 or later
* Mac OS X Snow Leopard 10.6.8 or later
Note: Mac OS X Leopard v10.5.x is not supported in this version of Parallels Desktop.