With time series spectroscopic observations taken with the Near-Infrared Spectrometer (NIRSPEC) at Keck II, we investigated the atmosphere of the close orbiting transiting extrasolar giant planet, HD 189733b. In particular, we intended to measure the dense absorption line forest around 2.3 μm, which is produced by carbon monoxide (CO). CO is expected to be present in the planetary atmosphere, although no detection of this molecule has been claimed yet. To identify the best-suited data analysis method, we created artificial spectra of planetary atmospheres and analysed them by three approaches found in the literature, the deconvolution method, data modelling via χ2 minimization and cross-correlation. As a result, we found that cross-correlation and χ2 data modelling show systematically a higher sensitivity than the deconvolution method. We analysed the NIRSPEC data with cross-correlation and detect CO absorption in the day-side spectrum of HD 189733b at the known planetary radial velocity semi-amplitude with 3.4σ confidence.