I searched the internet and CRC handbook but there were no complete information about the the solubility of ZrC4O8 in basic or acidic solutions. Does anybody know a reliable source for this kind of information?
Zr(IV) oxalate is considered highly insoluble in water (*). You may refer to signalled reference (**) for a rather convenient review comprising some literature data on the solubility product of zirconium oxalates and on the formation constant of oxalate complexes of zirconium. The solubility of Zr(IV) oxalate in aq. sol. can, in principle, be derived from such data, by further considering also the dissociation constants of oxalic acid, as discussed in several analytical chemistry textbooks (***).
(**) M. Illemassène (Vol. Ed.), W. Hummel (Chairman), G. Anderegg, L. Rao, I. Puigdomènech, O. Tochiyama, "Chemical Thermodynamics of Compounds and Complexes of U, Np, Pu, Am, Tc, Se, Ni and Zr With Selected Organic Ligands", book series: "Chemical Thermodynamics" (nº 9), OECD Nuclear Energy Agency / Elsevier, 2005, pp. 202-206.
(***) Cf. (e.g.): D.A. Skoog, D.M. West, “Fundamentals of Analytical Chemistry”, 3rd ed., Holt-Saunders Int. Eds., 1976, pp. 93-94.