We present an analysis of the relation between star formation rate (SFR) surface density (sigmasfr) and mass surface density of molecular gas (sigmahtwo), commonly referred to as the Kennicutt-Schmidt (K-S) relation, at its intrinsic spatial scale, i.e. the size of giant molecular clouds (10-150 pc), in the central, high-density regions of four nearby low-luminosity active galactic nuclei (AGN). We used interferometric IRAM CO(1-0) and CO(2-1), and SMA CO(3-2) emission line maps to derive sigmahtwo and HST-Halpha images to estimate sigmasfr. Each galaxy is characterized by a distinct molecular SF relation at spatial scales between 20 to 200 pc. The K-S relations can be sub-linear, but also super-linear, with slopes ranging from 0.5 to 1.3. Depletion times range from 1 and 2Gyr, compatible with results for nearby normal galaxies. These findings are valid independently of which transition, CO(1-0), CO(2-1), or CO(3-2), is used to derive sigmahtwo. Because of star-formation feedback, life-time of clouds, turbulent cascade, or magnetic fields, the K-S relation might be expected to degrade on small spatial scales (