Fintan Vallely, in his Handbook of Irish Traditional Music, refers to a single mid-19C. illustration where someone appears to be playing a large tambourine, using hand or stick (I'm not sure which)against the skin. This may or may not be a bodhran as we know it. As mentioned earlier, the word appears in Dineen's Irish dictionary (early 20 C.) with both drum and tray/winnow meanings. I've also seen it in P W Joyce's "English as we speak it in Ireland" . The fact that it is anglicised there (1910) suggests it was around for some time by then.
Vallely reckons its use as a drum was largely confined to the "Wren" (St. Stephen's Day celebrations) until Sean O Riada started using it in the early sixties.
Older bodhrans often had coins, pot-menders etc. inserted as rattles - and the instrument was often referred to as a tambourine. It is quite likely that some of this usage came via Salvation Army use.
p.s. I love that line about the turf-carrier.