There were a number of serial killers on the American frontier well before and after the period ended. The most bloody of these were the scalp hunters of the borderlands. One such killer was John Glanton, who figures prominently in McCarthy's Blood Meridian. Glanton was banished from Mexico for killing innocent Mexicans to collect their scalps. James Kirker was even more successful than Glanton, but no reputable accounts accuse him of killing too many people (so long as you don't count the hundreds of Native Americans he scalped).
The Cochise Cowboys were a later outlaw group in Arizona territory. Although they're most famous for their involvement in the Gunfight at the O.K. Corral in Tombstone, they killed 15 Mexican smugglers in the Skeleton Canyon massacre and dozens more in various raids.
These were a few of the more famous serial killers on the frontier but there's no shortage of people to list. The Harpe brothers, the Servant Girl Annihilator, the Bloody Benders, Jesse James... All were involved in shocking numbers of murders.
If you'd like to know more about the scalp hunters, The Scalp Hunter in the Borderlands 1835-1850 by Ralph A. Smith is the classic article.
You might be interested on some previous threads on serial killers in North America and Ancient Rome:
Ancient Roman Serial Killers
What is the oldest known case of a serial killer, and how were they dealt with? - 3 comments, over 1 month old.
A commenter gives a short summary about the actions of a Roman serial killer .
Were there any serial killers in Ancient Rome or during the Middle Ages? - 25 comments, over 1 year old.
The topmost comment talks about the mechanics of nobility getting away with serial killing in the Middle Ages and lower top-level comments discuss Ancient Roman examples.
North America
Were there well-documented cases of American serial killers before the turn of the century? - 7 comments, over 2 years old.
There isn't much deep analysis in this thread but there are a variety of name drops and wikipedia links.
Are there any records of murders/serial killings among Native American tribes prior to heavy European influence? - 3 comments, over 3 months old.
Despite being outside of your parameters, the commenters here both give large, sourced answers for Inuit and Pueblo examples of serial killers.
Other Serial Killers and Mass Murderers
Are there any records of serial killers in ancient times? If so, how were they found out and how were they dealt with? - 242 comments, over 1 year old.
This thread draws on examples from Ancient Rome, Ancient Greece, Medieval and Early Modern Europe, and "Medieval" India.
How old is the phenomena of spree shootings/killings - Did it rise with media such as Television or are there older accounts? - 22 comments, over 1 year old.
This thread draws on Ancient Roman and Malaysian examples to compare to more modern occurrences.
Thank you for your replies and to OP for the question. I've often thought about the topic of pre 20th century serial killers and how common they might of been. Was there actually any awareness of the phenomenon in the past or did it take until the Victorian period for people to catch on?