Yes. There were a number of ways physicians could diagnose twins other than with an ultrasound. I will answer this question predominantly as a practicing physician, as I think it's less of a historical question, and more of a medical question.

Clinical suspicion would most commonly be aroused by finding that a woman was measuring large for her dates, based on her fundal height. Immediate confirmation could sometimes be obtained via auscultation (with a stethoscope) of two separate heart rates (each going at a different rate from each other, and from the mom). Electrocardiography had been reported to be used as well, though I am not sure how wide-spread this was in clinical practice in that era.

Otherwise, twins could often be confirmed later in the pregnancy (ie: the third trimester) by simply palpating the woman's abdomen. Towards the end of pregnancy, it is quite easy to feel fetal body parts through the mother's abdominal wall (this is still how fetal position is usually assessed at antenatal visits). With twins, you can often feel two separate heads for example.

There are relatively few open-access medical articles on this topic from that era; however, here is one I found. The relevant parts are under the results section. This article is not ideal as it was conducted in an era when ultrasound was available; however it was nowhere near as widespread at it is today, and reviewing this article you'll see that only 9 of the 94 sets were initially diagnosed with ultrasound. The most common method of initial diagnosis was clinical suspicion based on being large for dates.