  Fast magnetic reconnection plays a fundamental role in driving explosive
dynamics and heating in the solar chromosphere. The reconnection time scale of
traditional models is shortened at the onset of the coalescence instability,
which forms a turbulent reconnecting current sheet through plasmoid
interaction. In this work we aim to investigate the role of partial ionisation
on the development of fast reconnection through the study of the coalescence
instability of plasmoids. Unlike the processes occurring in fully ionised
coronal plasmas, relatively little is known about how fast reconnection
develops in partially ionised plasmas of the chromosphere. We present 2.5D
numerical simulations of coalescing plasmoids in a single fluid
magnetohydrodynamic (MHD) model, and a two-fluid model of a partially ionised
plasma (PIP). We find that in the PIP model, which has the same total density
as the MHD model but an initial plasma density two orders of magnitude smaller,
plasmoid coalescence is faster than the MHD case, following the faster thinning
of the current sheet and secondary plasmoid dynamics. Secondary plasmoids form
in the PIP model where the effective Lundquist number $S = 7.8 \cdot 10^3$, but
are absent from the MHD case where $S = 9.7 \cdot 10^3$: these are responsible
for a more violent reconnection. Secondary plasmoids also form in linearly
stable conditions as a consequence of the non-linear dynamics of the neutrals
in the inflow. In the light of these results we can affirm that two-fluid
effects play a major role on the processes occurring in the solar chromosphere.
