Using the Oxford Short Wavelength Integral Field specTrograph (SWIFT), we trace radial variations of several initial mass function (IMF) sensitive absorption features within Coma cluster galaxies. We observe the two central brightest cluster galaxies (BCGs) NGC4889, NGC4874, and the BCG in the south-west group NGC4839, as well as the fast rotator NGC4873 as an `ordinary' control. We present radial measurements of the IMF-sensitive features sodium NaI, calcium triplet CaT and iron-hydride FeH0.99, along with the magnesium MgI0.88 and titanium oxide TiO0.89 features. We employ two separate methods for both telluric correction and sky-subtraction around the faint FeH feature to verify our data reduction processes. Within NGC4889 we find strong gradients of NaI and CaT but a flat FeH profile, which from comparing to stellar population synthesis models, suggests an old, alpha-enhanced population with a Chabrier, or even bottom-light IMF. The age and abundance is in line with previous studies but the Chabrier IMF is in conflict with recent evidence for an increased IMF slope with increased velocity dispersion. We measure flat NaI and FeH profiles within NGC4874 and NGC4873 and also infer Chabrier IMFs. In contrast, within NGC4839 we measure both strong NaI and strong FeH, which may be evidence for a bottom-heavy IMF slope. The IMFs we infer for these galaxies are supported by published dynamical modelling results and optical index measurements. Our results indicate the possibility of different formation scenarios for the BCGs. We stress that IMF constraints in massive galaxies should be corroborated by further spectral coverage and independent methods on a galaxy-by-galaxy basis.