"He would prefer to have a different job."

Translation: On wolałby mieć inną pracę.

[Ten_Pies_I_Brew]

I don't know why, but I had an urge to use the genitive here. Is wolałby mieć innej pracy possible as well, or is that outright wrong?

[br0d4]

In affirmative phrase it is plainly wrong. The verb "mieć" requires noun in accusative.

But in phrases with negation, the accusative is replaced by genitive: "On nie wolałby mieć innej pracy".