Using the Oxford Short Wavelength Integral Field specTrograph (SWIFT), we trace radial variations of initial mass function (IMF) sensitive absorption features of three galaxies in the Coma cluster. We obtain resolved spectroscopy of the central 5kpc for the two central brightest-cluster galaxies (BCGs) NGC4889, NGC4874, and the BCG in the south-west group NGC4839, as well as unresolved data for NGC4873 as a low-$sigma_*$ control. We present radial measurements of the IMF-sensitive features sodium NaI$_{rm{SDSS}}$, 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 analysis. Within NGC4889 we find strong gradients of NaI$_{rm{SDSS}}$ 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 normal IMF is in contrast to recent results suggesting an increased IMF slope with increased velocity dispersion. We measure flat NaI$_{rm{SDSS}}$ and FeH profiles within NGC4874 and determine an old, possibly slightly $alpha$-enhanced and Chabrier IMF population. We find an $alpha$-enhanced, Chabrier IMF population in NGC4873. Within NGC4839 we measure both strong NaI$_{rm{SDSS}}$ and strong FeH, although with a large systematic uncertainty, suggesting a possible heavier IMF. The IMFs we infer for these galaxies are supported by published dynamical modelling. We stress that IMF constraints should be corroborated by further spectral coverage and independent methods on a galaxy-by-galaxy basis.
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