Pocket AVR Programmer + PIC32MX
As, people before me said, you can't do it with AVR-specific programmer. But a lot of different programmers can be utilised with PIC32MX and pic32prog utility. Some of the supported programmers (both open source and proprietary) include:


Microchip PICkit2
Microchip PICkit3 with scripting firmware
Olimex ARM-USB-Tiny, ARM-USB-Tiny-H and ARM-USB-OCH-H JTAG adapters
Olimex MIPS-USB-OCH-H JTAG adapter
Bus Blaster v2 JTAG adapter from Dangerous Prototypes
Flyswatter JTAG adapter from TinCanTools


For example Bus Blaster is completely open and you can build it yourself.