Will a TIP42 suffice for this project that calls for a BC559 (transistors)?
No. TIP42 is a power transistor. It might do the job, but I think h(FE) is just too low and it is way too expensive. You want a general purpose PNP transistor like BC556, BC557, BC558, BC327, BC328, ...

Important parameters are:


power dissipation;
collector current;
current gain (hFE)
collector emitter voltage;