The geomagnetic field variations on the continent of Africa are still largely undeciphered for the past two millennia. In spite of archaeological artefacts being reliable recorders of the ancient geomagnetic field strength, only few data have been reported for this continent so far. Here we use the Thellier-Coe and calibrated pseudo-Thellier methods to recover archaeointensity data from Burkina Faso and Ivory Coast (West Africa) from well-dated archaeological artefacts. By combining our 18 new data with previously published data from West Africa, we construct a reference curve for West Africa for the past 2000 years. To obtain a reliable curve of the archaeointensity variation, we evaluate a penalized smoothing spline fit and a stochastic modelling method, both combined with a bootstrap approach. Both intensity curves agree well, supporting the confidence in our proposed intensity variation during this time span, and small differences arise from the different methodologies of treating data and uncertainties. Two prominent peaks at around 740 AD and 1050 AD appear to be common in ours and several reference curves from other locations, indicating a general westward movement from China to Hawaii of a rather stable feature of the geomagnetic field. However, independent smaller peaks that do not correlate in different locations may hint to localized expressions of the geomagnetic field as a result of temporarily varying non-dipole sources.