To go back to the origninal question I had, I wanted know if using a ULN2003A would OK without using a clamp diode to suppress the flyback voltage on a relay that needs a current of 77mA to close.

The concensus is, for the most part, I should be OK. The only correction I need make is to connect pin 9.

In addition, to be sure of myself, I will set the PIC up to cycle the relay every second and let it run for a week. The cycle of the relay is something like 6-8 times per day and if I let it cycle for one week, it should get something like 300,000 cycles. I think if it passes that test, there should not be a problem with reliability.