  We report on the anisotropic properties of Pauli-limited superconductivity
(SC) and antiferromagnetism (AFM) in the solid solutions CeCo(In_{1-x}Zn_x)_5
(x<=0.07). In CeCo(In_{1-x}Zn_x)_5, the SC transition temperature T_c is
continuously reduced from 2.3 K (x=0) to ~1.4 K (x=0.07) by doping Zn, and then
the AFM order with the transition temperature of T_N~2.2 K develops for x
larger than ~0.05. The present thermal, transport and magnetic measurements
under magnetic field B reveal that the substitution of Zn for In yields little
change of low-temperature upper critical field \mu_0H_{c2} for both the
tetragonal a and c axes, while it monotonically reduces the SC transition
temperature T_c. In particular, the magnitudes of \mu_0H_{c2} at the nominal Zn
concentration of x = 0.05 (measured Zn amount of ~0.019) are 11.8 T for B||a
and 4.8 T for B||c, which are as large as those of pure compound though T_c is
reduced to 80% of that for x=0. We consider that this feature originates from a
combination of both an enhanced AFM correlation and a reduced SC condensation
energy in these alloys. It is also clarified that the AFM order differently
responds to the magnetic field, depending on the field directions. For B||c,
the clear anomaly due to the AFM transition is observed up to the AFM critical
field of ~5 T in the thermodynamic quantities, whereas it is rapidly damped
with increasing B for B||a. We discuss this anisotropic response on the basis
of a rich variety of the AFM modulations involved in the Ce115 compounds.
