  Two triangular lattice antiferromagnets Sr$_3$Co(Nb,Ta)$_2$O$_9$ with an
effective $j_{\rm eff}=1/2$ of Co$^{2+}$ are synthesized and their magnetic
properties are investigated via magnetization and heat capacity measurements.
The leading in-plane antiferromagnetic exchange coupling is estimated to be
$J/k_{\rm B} \simeq 4.7$ K and 5.8 K, respectively. Both the compounds feature
two-step magnetic transitions at low temperatures [($T_{\rm N1} \simeq 1.47$ K
and $T_{\rm N2} \simeq 1.22$ K) and ($T_{\rm N1} \simeq 0.88$ K and $T_{\rm N2}
\simeq 0.67$ K), respectively], driven by weak easy-axis anisotropy. Under
magnetic field Sr$_3$CoNb$_2$O$_9$ evinces a plateau at $1/3$ magnetization.
Interestingly, the high field magnetization of Sr$_3$CoTa$_2$O$_9$ reveals an
exotic regime (between $H_{\rm S1}$ and $H_{\rm S2}$), below the fully
polarized state in which the heat capacity at low temperatures is governed by a
power law ($C_{\rm p} \propto T^{\alpha}$) with a reduced exponent $\alpha
\simeq 2$. These results demonstrate an unusual field induced state with
gapless excitations in the strongly frustrated magnet Sr$_3$CoTa$_2$O$_9$. The
complete $T-H$ phase diagram is discussed for both the compounds.
