We present an analysis of the constraints on the amplitude of primordial non-Gaussianity of local type described by the dimensionless parameter fNL. These constraints are set by the auto-correlation functions (ACFs) of two large scale structure probes, the radio sources from NRAO VLA Sky Survey (NVSS) and the QSO catalogue of Sloan Digital Sky Survey Release Six (SDSS DR6 QSOs), as well as by their cross-correlation functions (CCFs) with the cosmic microwave background (CMB) temperature map (Integrated Sachs-Wolfe effect). Several systematic effects that may affect the observational estimates of the ACFs and of the CCFs are investigated and conservatively accounted for. Our approach exploits the large-scale scale-dependence of the non-Gaussian halo bias. The derived constraints on {fNL} coming from the NVSS CCF and from the QSO ACF and CCF are weaker than those previously obtained from the NVSS ACF, but still consistent with them. Finally, we obtain the constraints on fNL = 53±25 (1 σ) and fNL = 58±24 (1 σ) from NVSS data and SDSS DR6 QSO data, respectively.