According to LLM Guide, only two schools in the United States offer Master of Laws in construction law: the University of Oregon and Mississippi College's School of Law. The University of Oregon specializes in environmental law. Among a variety of LL.M. options, all relating to the environment, is an LL.M. in green building and construction (that is, constructing buildings in an environmentally friendly way).
A private Christian school, Mississippi College trains students from overseas to work in the global legal construction practice. American students can attend the law school, but only if they earned their degree from a college outside the United States.
Several universities in English-speaking countries offer LL.M. degrees in construction law, such as the University of Melbourne in Australia and the University of Salford in England. As long as the school is ABA (American Bar Association) accredited, you can take the bar in most states even if you earned your LL.M. overseas. However, it is best to check if the school is accredited and that your state recognizes an overseas degree before enrolling. Because most overseas schools teach the laws of their countries, it's a good idea to research their curriculums thoroughly.
Robert Gordon University of Aberdeen in Scotland holds online classes in construction law which can be accessed from anywhere in the world by anyone with an account and an internet connection. It takes three years to earn an LL.M. from the school, instead of one or two as it would in the U.S., though if you have former legal training you can be exempted from certain courses. Study focuses on UK law, especially in England, Wales and Scotland.
Despite the scarcity of Master of Laws degrees in construction law, lawyers can practice construction law in the U.S. by earning their LL.M. in a similar field, such as property law.
For example, Washington University of Saint Louis has several courses in construction law; a student would earn his LL.M. in economics law but could practice as a specialist in construction law after graduation. Searching law school websites for courses in construction law may turn up many classes. If you find some, you can mail the registrar and ask about the possibility of practicing construction law with the degrees they offer.