A couple of the ATtiny processors do not have SPI, but all others do. Note that if you do use the in-circuit programming capability of the controllers, you will lose the other functionalities of the pins. The other alternative is to program them externally using adapters. The PonyProg is an overall good programmer, an dit has a list of supported microcontrollers.
Another alternative (simpler programmer HW) is the SP12. Just do a Google search for SP12. I have used it as well, and it works!