An hydrolysis of the P-Cl bonds of the carbophosphazene [{NC(NMe$_2$)}{NPCl}$_2$] (L) in the presence of hydrated lanthanide(III) nitrates in a dichloromethane and methanol (2 : 1) solvent mixture afforded a series of novel 1D coordination polymers: {Ln(L$^{HPO_2}$)$_3$(NO$_3$)$_2$(CH$_3$OH)(H$_2$O)} (Cl)]$_n$ {where Ln(III) = Gd (1), Tb (2), Dy (3), or Er (4) and L is the hydrolyzed carbophosphazene (L) ligand}. X-ray crystallographic analysis revealed that complexes 1-4 are isostructural and crystallized in the monoclinic crystal system having P2$_1$/$c$ space group. The coordination polymers are formed because of the involvement of the geminal P(O)(OH) moieties of the carbophosphazene ligand. Each lanthanide(III) ion is 9-coordinate (9O) in a distorted muffin geometry. Magnetic measurements revealed that both Dy$^{III}$ and Er$^{III}$ analogues exhibit field-induced single-molecule magnet (SMM) behavior at 0.8 kOe and 2.2 k Oe, respectively. At such dc fields, the dynamic magnetic susceptibility displays complex behavior with a triple magnetic relaxation contribution for 3, while two contributions were identified for 4. The observed static and dynamic magnetic behavior for complexes 1-4 were further rationalized with the aid of BS-DFT and CASSCF/SO-RASSI/SINGLE_ANISO calculations.