  We study the quantum phase transitions in the nickel pnctides,
CeNi$_{2-\delta}$(As$_{1-x}$P$_{x}$)$_{2}$ ($\delta$ $\approx$ 0.07-0.22). This
series displays the distinct heavy fermion behavior in the rarely studied
parameter regime of dilute carrier limit. We systematically investigate the
magnetization, specific heat and electrical transport down to low temperatures.
Upon increasing the P-content, the antiferromagnetic order of the Ce-4$f$
moment is suppressed continuously and vanishes at $x_c \sim$ 0.55. At this
doping, the temperature dependences of the specific heat and longitudinal
resistivity display non-Fermi liquid behavior. Both the residual resistivity
$\rho_0$ and the Sommerfeld coefficient $\gamma_0$ are sharply peaked around
$x_c$. When the P-content reaches close to 100\%, we observe a clear
low-temperature crossover into the Fermi liquid regime. In contrast to what
happens in the parent compound $x$ = 0.0 as a function of pressure, we find a
surprising result that the non-Fermi liquid behavior persists over a nonzero
range of doping concentration, $x_c<x<0.9$. In this doping range, at the lowest
measured temperatures, the temperature dependence of the specific-heat
coefficient is logarithmically divergent and that of the electrical resistivity
is linear. We discuss the properties of
CeNi$_{2-\delta}$(As$_{1-x}$P$_{x}$)$_{2}$ in comparison with those of its 1111
counterpart, CeNi(As$_{1-x}$P$_{x}$)O. Our results indicate a non-Fermi liquid
phase in the global phase diagram of heavy fermion metals.
