Do biplanes need bigger tail coeefficients than monoplanes (of equal wing area)?
Here's where building free flight models and testing them in cross wind conditions is very helpful. As a designer, it is important to consider wing and tail functionality. Many "tailless" designs, such as deltas, have adequate stability without a separate and distinctive "tail". Reducing chord and increasing aspect increases the need for a separate, stabilizing "tail". Some designs put the "tail"(canard) in front to decrease stability and increase maneuverability.
You may find biplanes need a smaller vertical volume than a mono plane of similar wing area. This is consistent with designs of 100 years ago, where "slab sides" also aided in lateral stability.
The testing for for vertical tail volume can be done by releasing the plane in a cross wind, and seeing if it "points" into the wind or turns away. Many mono plane designs, particularly with excessive dihedral "effect", will roll and turn away from the wind. Biplanes seem to be less prone to this, possibly due to a shielding effect of the lower wing to the upper wing from the cross wind.
Tests for adequate horizontal stabilizer size will include adequate directional and static stabilility, but also there is one very important aspect of inertial rotation effect for larger aircraft. The horizontal stabilizer needs to be larger to arrest pitching momentum before it exceeds stall AOA and effectively reduce AOA faster than it increases from relative wind shift from downward acceleration as the plane "sinks" from loss of lift. This issue is much less common in GA sized aircraft unless aft CG limit is abused.
One may also find a wider wing, or 2 "staggered" wings, reduces the need for a horizontal stabilizer. But keep in mind using the wing as a stabilizer may reduce its efficiency of lifting, it's primary task. Notice "flying wings" have yet to replace the classic "wing and tail" design of modern sailplanes, though they can be very stylish looking.
There are many factors which go into the sizing of the vertical and horizontal stabilizer. For a (low Mach number) recreational aircraft, adequate "anhedralling" (side area below the CG) helps eliminate the need for excessive V stab area, as well as a longer torque arm (longer fuselage).
Evaluation of 120 years of existing and proven aircraft design, and choosing the parameters of desired performance, may be more useful than "rule of thumb". Essentially, it is a trade-off of stability, maneuverability, and drag before software is needed to keep one from crashing.