Attenuation coefficient estimation has the potential to be a useful tool for placental tissue characterization. A current challenge is the presence of inhomogeneities in biological tissue that result in a large variance in the attenuation coefficient estimate (ACE), restricting its clinical utility. In this work, we propose a new Attenuation Estimation Region Of Interest (AEROI) selection method for computing the ACE based on the (i) envelope signal-to-noise ratio deviation and (ii) coefficient of variation of the transmit pulse bandwidth. The method was first validated on a tissue-mimicking phantom, for which an 18%-21% reduction in the standard deviation of ACE and a 14%-24% reduction in the ACE error, expressed as a percentage of reported ACE, were obtained. A study on 59 post-delivery clinically normal placentas was then performed. The proposed AEROI selection method reduced the intra-subject standard deviation of ACE from 0.72 to 0.39 dB/cm/MHz. The measured ACE of 59 placentas was 0.77 ± 0.37 dB/cm/MHz, which establishes a baseline for future studies on placental tissue characterization.