(Abridge) The relationship between coronal line (CL) emission and nuclear activity in active galactic nuclei (AGNs) is analyzed, for the first time, based on NIR spectra. The 8 CLs studied, of Si, S, Fe, Al and Ca elements and corresponding to ionization potentials (IP) in the range 125-450 eV, are detected in 67% (36 AGNs) of the sample. The four most frequent CLs - [SiVI] 19630AA, [SVIII] 9913AA, [SIX] 12520AA and [SiX] 14320AA, - display a narrow range in luminosity, with most lines located in the interval logL 39-40 erg/s. We found that the non-detection is largely associated with either a lost of spatial resolution or increasing object distance. Yet, there are AGNs where the lack of CLs may be genuine and reflect an AGN ionising continuum lacking photons below a few keV. The FWHM of the lines profiles increases with increasing IP up to energies around 300 eV, where a maximum in the FWHM is reached. For higher IP lines, the FWHM remains nearly constant or decreases with increasing IP. We ascribe this effect to an increasing density environment as we approach to the innermost regions of the AGN, where densities above the critical density of the CLs with IP larger than 300 eV are reached. This sets a strict range limit for the density in the boundary region between the narrow and the broad region of 10^8 - 10^9 cm^{-3}. A relationship between the luminosity of the coronal lines and that of the soft and hard X-ray emission and the soft X-ray photon index is observed: the coronal emission becomes stronger with both increasing x-ray emission (soft and hard) and steeper X-ray photon index. Thus, photoionization appears as the dominant excitation mechanism. These trends hold when considering Type 1 sources only; they get weaker or vanish when including Type 2 sources, very likely because the X-ray emission measured in the later is not the intrinsic ionising continuum.
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