Not at that facility, and the reason is practical rather than arbitrary.
St. Louis City Justice Center is a short-term holding facility. It houses people who are awaiting trial, awaiting sentencing, or serving short sentences before being transferred to a longer-term facility. Short-term city and county jails simply do not have the administrative infrastructure or the policy framework for inmate marriages. There is no chaplain program set up for ceremonies, no warden protocol for approving marriage requests, and no precedent for it happening there. It is not a question of working around the requirement that you both appear. The facility just does not do marriages.
Inmate marriages are reserved for longer-term placements at state prisons or federal facilities, and even there, the bar is meaningful. The inmate needs a clean disciplinary record, has typically served a meaningful portion of their sentence, and has to submit a formal petition to the warden, who reviews and approves or denies it. The process is real, and people do get married in those settings, but it requires the right facility and the right circumstances.
If your person is at St. Louis City Justice Center awaiting trial or sentencing and eventually gets transferred to a state prison for a longer sentence, that is when the conversation about marriage becomes a realistic one to have with facility staff and the chaplain.
In the meantime, the most meaningful things you can do are stay connected through letters, calls, and visits, and be there when the situation changes. The marriage can happen when the circumstances allow for it to happen properly.