SPIDERS (SPectroscopic IDentification of eROSITA Sources) is an SDSS-IV survey running in parallel to the eBOSS cosmology project. SPIDERS will obtain optical spectroscopy for large numbers of X-ray-selected AGN and galaxy cluster members detected in wide area eROSITA, XMM-Newton and ROSAT surveys. We describe the methods used to choose spectroscopic targets for two sub-programmes of SPIDERS: X-ray selected AGN candidates detected in the ROSAT All Sky and the XMM-Newton Slew surveys. We have exploited a Bayesian cross-matching algorithm, guided by priors based on mid-IR colour-magnitude information from the WISE survey, to select the most probable optical counterpart to each X-ray detection. We empirically demonstrate the high fidelity of our counterpart selection method using a reference sample of bright well-localised X-ray sources collated from XMM-Newton, Chandra and Swift-XRT serendipitous catalogues, and also by examining blank-sky locations. We describe the down-selection steps which resulted in the final set of SPIDERS-AGN targets put forward for spectroscopy within the eBOSS/TDSS/SPIDERS survey, and present catalogues of these targets. We also present catalogues of ~12000 ROSAT and ~1500 XMM-Newton Slew survey sources which have existing optical spectroscopy from SDSS-DR12, including the results of our visual inspections. On completion of the SPIDERS program, we expect to have collected homogeneous spectroscopic redshift information over a footprint of ~7500 deg$^2$ for >85 percent of the ROSAT and XMM-Newton Slew survey sources having optical counterparts in the magnitude range 17<r<22.5, producing a large and highly complete sample of bright X-ray-selected AGN suitable for statistical studies of AGN evolution and clustering.
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