Do biplanes need bigger tail volume coefficients than monoplanes?
Tail volume is a measure for the ability of the tail to compensate for the destabilizing pitch moment created by the wing in case of the horizontal tail and for adverse yaw in case of the vertical tail. This pitch moment is proportional to the square of the wing chord (one factor comes from the area, the second from the lever arm), so if you compare two otherwise equal designs, one of which is a biplane and the other a monoplane of twice the chord, the dimensionful horizontal tail volume (expressed as tail surface times tail lever arm) of that monoplane needs to be twice that of the biplane. To counter adverse yaw, however, the dimensionful vertical tail volume is the same.

Tail volume is normally made dimensionless by referencing it to the wing area and the mean aerodynamic chord (for the horizontal) or wing span (for the vertical tail). Since the area of both designs is the same and the MAC of the monoplane twice as large as that of the biplane, both dimensionless horizontal and vertical tail volumes become equal even though the dimensionful horizontal tail volume of the monoplane is twice as large.

However, if you compare wings of the same aspect ratio (which might be a better basis), both the chord and the wing span of the monoplane are larger by a factor of √2 but there is only one wing to consider versus two in case of the biplane. Now the dimensionful horizontal and vertical tail volumes for the monoplane are larger by a factor of √2.

Only when you make the chord of both wings equal (doubling the span of the monoplane in the process) will the dimensionful horizontal tail volume of both designs be equal but now the vertical tail volume needs to be twice as large.

Wing stagger with the same incidence on both wings would move the biplane closer to the monoplane with twice the chord whereas a lower incidence on the rear wing would indeed create that reflex effect and reduce the instability of the wing. Still, you need control power to change angle of attack quickly enough for maneuvering, so I would be careful with any further reduction of tail volume even if the staggered biplane wing by itself is stable already.