Are there any “complete” languages in $coNP -NP$?

Question

Suppose $coNP \neq NP$

language B would be called "complete" in $coNP-NP$ if:

1. $B\in coNP - NP$
2. $A\in coNP-NP \implies A\leq_pB$

Are there any "complete" languages in $coNP - NP$?