The Large Magellanic Cloud (LMC) contains the nearest large extragalactic population of planetary nebulae (PNe). A shallow viewing angle and low interstellar reddening towards the LMC potentially means a larger, more complete flux-limited population can be assembled than for any other galaxy. These advantages appear to be reflected by the small gap between the catalogued ($sim$700 PNe) and estimated ($1000pm250$ PNe) population size. With more detailed multi-wavelength studies the catalogued number of LMC PNe may fall, potentially widening this gap. We demonstrate here that the gap can be further bridged with improved optical and near-infrared imaging surveys. We present three [O III]-selected PNe discovered from ESO WFI observations of the 30 Doradus region and one serendipitous discovery from near-infrared Vista Magellanic Cloud (VMC) survey observations. The WFI PNe have resolved [O III] and H$alpha$ nebulae that verify their PN nature and their [O III] fluxes place them 6--7 mag ($m_{5007}=20$--21 mag) fainter than the bright-end of the planetary nebula luminosity function (PNLF). Their faintness, small angular size and surrounding complex emission-line background explains why previous H$alpha$ surveys of the region did not select them. We estimate there may be as many as 50--75 similar PNe awaiting discovery in the central $5times5$ degrees of the LMC. The VMC survey routinely detects PNe as red resolved nebulae that may allow some of this expected population to be recovered without traditional narrow-band imaging surveys. We demonstrate this potential with the first new VMC-selected PN which has a rare Wolf-Rayet [WC9]--[WC11] central star.