This paper proposes two simple and powerful algorithms to automatically paint Celtic knots with aesthetic colors. The shape of the knot is generated from its dual graph as presented in [KC03]. The first technique uses rules derived from two-colors harmony studies in a Color Order System to select harmonious color pairs. We show that it can efficiently reproduce color combinations utilized in ancient and modern Celtic design. The second technique aims at creating knots with a rainbow type colorization that can be seen in modern Celtic art. The user controls a few parameters like the number of desired different hues, or the average brightness and saturation expected, by defining an ellipse in the color space. The program then accordingly selects a series of colors. In both cases, we apply rules issued from prior Color Science studies. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Color, shading, shadowing, and texture