Conductive atomic force microscopy (C-AFM) is used to characterise the nanoscale electrical properties of many conducting and semiconducting materials. We investigate the effect of single walled carbon nanotube (SWCNT) modification of commercial Pt/Ir cantilevers on the sensitivity and image stability during C-AFM imaging. Pt/Ir cantilevers were modified with small bundles of SWCNTs via a manual attachment procedure and secured with a conductive platinum pad. AFM images of topography and current were collected from heterogeneous polymer and nanomaterial samples using both standard and SWCNT modified cantilevers. Typically, achieving a good current image comes at the cost of reduced feedback stability. In part, this is due to electrostatic interaction and increased tip wear upon applying a bias between the tip and the sample. The SWCNT modified tips displayed superior current sensitivity and feedback stability which, combined with superior wear resistance of SWCNTs, is a significant advancement for C-AFM.