I would use an ULN2003 for six relays. You can connect it directly to the 8051 outputs.

But that will not solve your problem. You have to add inverters between the '51 and the ULN to fix that. Or perhaps it's not a problem - if you set the pins low as the first thing your code does, perhaps that's good enough?

Best regards,

Mikkel C. Simonsen