What are the visa options for an unmarried couple with a child in Thailand?

Tod Daniels is seeking information on visa options upon arrival in Bangkok for himself and his son, who are entering on a tourist visa, while his partner holds a work permit. Comments indicate that there are limited options available for unmarried couples, particularly noting that having a work permit or a child together may not qualify them for a long-term visa. One comment mentions a foreign child visa that has a financial requirement.