Welcome to Just Answer. Alois is a baby name found all over Germany, not just in Bavaria.
There is no online record of his birth in either Germany or Austria.
Have you checjed marriage records in Colorafo? They are not online. Since according to the 1900 census their first daughter was born in January 1884 and he said he arrived in 1881 and Mary arrived in 1882, the marriage would have been between 1882 and 1884. Marriage records are available from the district court clerks. Here is their contact information http://www.courts.state.co.us/Courts/District/Choose.cfm
Looking forward to hearing from you,
Hello, and thank you for your response. Would these marriage records provide the information I am looking for? - That is, information about Alois's parents, which I could use to trace my family history back past Alois.
Frankly, there is no way to know exactly what information the records would provide until you actually see them. Marriage records generally give date and place of birth as well as parents' names. However, there were few state-wide requirements so some records will be more complete than others. None of them are online. Most family historians want to obtain a copy just to have it, regardless of what it contains. It will definitely contain the date of marriage, which doesn't appear to be something that is currently known.