Coordinate interleaved orthogonal design (CIOD) using four transmit antennas provides full diversity, full rate (FDFR) properties with low decoding complexity. However, the constellation expansion due to the coordinate interleaving of the rotated constellation results in peak to average power ratio (PAPR) increase. In this paper, we propose two signal constellation design methods which have low PAPR. In the first method we propose a signal constellation by properly selecting the signal points among the expanded square QAM constellation points, based on the co-prime interleaving of the first coordinate signal. We design a regular interleaving pattern so that the coordinate distance product (CPD) after the interleaving becomes large to get the additional coding gain. In the other method we propose a novel constellation with low PAPR based on the clipping of the rotated square QAM constellation. Our proposed signal constellations show much lower PAPR than the ordinary rotated QAM constellations for CIOD.