That adapter (PLMQ7000-100NC for an EPM7128A in a TQFP100 package) is flagged as obsolete at all distributors I can find. You may find it surplus/used somewhere (like eBay?). This adapter is ONLY for use with the Altera Programming Unit (PL-APU) or the PL-ASAP2/PL-MPU (an IDE add in board!). Both are also flagged as obsolete. So unless you already have these I think you are SOL.
There are current third party programmers that still support Altera EPM7k devices in programming adapters OUT OF CIRCUIT. So you would have to remove your TQFP100 devices from your board(s) to program or read them.
Xeltek (www.xeltek.com) has programmers (eg, SuperPro 7500) that support the EPM7128A device and with the appropriate TQFP100 adapter would allow programming/reading/writing/verifying your EPM7128A device. It is a currently available product from them.
Personally I would go with the third party programmer solution if you can't come up with the original POF files from the manufacturer. It will be the only way to reliably duplicate existing physical parts.
If you have the POF file ideally programming the boards via a 10p JTAG header would be optimal, but if the original board is not designed to allow that it is probably not a reasonable option.
Good luck.