An investigation of the structural, thermodynamic, and electronic transport properties of the isoelectronic chemical substitution series Ce(Pd$_{1-x}$Ni$_x$)$_2$P$_2$ is reported, where a possible ferromagnetic quantum critical point is uncovered in the temperature - concentration ($T-x$) phase diagram. This behavior results from the simultaneous contraction of the unit cell volume, which tunes the relative strengths of the Kondo and RKKY interactions, and the introduction of disorder through alloying. Near the critical region at $x_{rm{cr}}$ $approx$ 0.7, the rate of contraction of the unit cell volume strengthens, indicating that the cerium $f$-valence crosses over from trivalent to a non-integer value. Consistent with this picture, x-ray absorption spectroscopy measurements reveal that while CePd$_2$P$_2$ has a purely trivalent cerium $f$-state, CeNi$_2$P$_2$ has a small ($<$ 10 %) tetravalent contribution. In a broad region around $x_{rm{cr}}$, there is a breakdown of Fermi liquid temperature dependences, signaling the influence of quantum critical fluctuations and disorder effects. Measurements of clean CePd$_2$P$_2$ furthermore show that applied pressure has a similar initial effect to alloying on the ferromagnetic order. From these results, CePd$_2$P$_2$ emerges as a keystone system to test theories such as the Belitz-Kirkpatrick-Vojta model for ferromagnetic quantum criticality, where distinct behaviors are expected in the dirty and clean limits.
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