The fraction of core-collapse supernovae (CCSNe) occurring in the central regions of galaxies is not well constrained at present. This is partly because large-scale transient surveys operate at optical wavelengths, making it challenging to detect transient sources that occur in regions susceptible to high extinction factors. Here we present the discovery and follow-up observations of two CCSNe that occurred in the luminous infrared galaxy (LIRG) NGC 3256. The first, SN 2018ec, was discovered using the ESO HAWK-I /GRAAL adaptive optics seeing enhancer, and was classified as a Type Ic with a host galaxy extinction of AV = 2:1+0:3 0:1 mag. The second, AT 2018cux, was discovered during the course of follow-up observations of SN 2018ec, and is consistent with a subluminous Type IIP classification with an AV = 2:1 +/- 0:4 mag of host extinction. A third CCSN, PSN J10275082 4354034 in NGC 3256, was previously reported in 2014, and we recovered the source in late-time archival Hubble Space Telescope imaging. Based on template light curve fitting, we favour a Type IIn classification for it with modest host galaxy extinction of AV = 0:3+0:4 0:3 mag. We also extend our study with follow-up data of the recent Type IIb SN 2019lqo and Type Ib SN 2020fkb that occurred in the LIRG system Arp 299 with host extinctions of AV = 2:1 +0:1 0 :3 and AV = 0:4 +0:1 0 :2 mag, respectively. Motivated by the above, we inspected, for the first time, a sample of 29 CCSNe located within a projected distance of 2.5 kpc from the host galaxy nuclei in a sample of 16 LIRGs. We find, if star formation within these galaxies is modelled assuming a global starburst episode and normal IMF, that there is evidence of a correlation between the starburst age and the CCSN subtype. We infer that the two subgroups of 14 H-poor (Type IIb /Ib /Ic /Ibn) and 15 H-rich (Type II /IIn) CCSNe have di fferent underlying progenitor age distributions, with the H-poor progenitors being younger at 3 sigma significance. However, we note that the currently available sample sizes of CCSNe and host LIRGs are small, and the statistical comparisons between subgroups do not take into account possible systematic or model errors related to the estimated starburst ages.