Single children have not been shown to be at increased risk of abuse. All the other listed answers are associated with increased stress on the family and have been shown to increase the likelihood of abuse.
There are certain social, parental and child indicators that statistically put children at a higher risk for abuse. Some of them are as obvious as a parent abusing a spouse while some are more subtle like separation of mother's parents. It is important for the treating physician to screen for these factors to identify situations of child abuse.
Kempe et al. provide and article which is an adaption from a lecture given in 1970 and gives a broad overview of child abuse. There are a few teaching points that are relavent to this question. Kempe discusses the idea that certain children are more vulnerable to abuse (hyperactive, precocious, premature, adopted, and step child). He also points out the act of abuse is a final common pathway of conflict when there is a problem with the parent or baby and for this to occur there must be; potential for abuse, certain characteristics of a certain child as seen by the particular parent, and conflict.
Rockwood and Wilkins' chapter on child abuse includes a list of parental, social, and child risk factors. A few from each group include: Parental- age <20 years, lower education, history of psychiatric disease; Social- job loss, family death, job loss, unplanned births, high levels of stress; Child- age <3 years, premature, stepchildren, handicapped.
Illustration A is a table showing some of the clinical findings in child abuse.
Kempe CH. Paediatric implications of the battered baby syndrome. Arch Dis Child. 1971 Feb;46(245):28-37. PubMed PMID:; PubMed Central PMCID: PMC1647584.
PMID:5555488 (Link to Abstract)
Schwend RM, Blakemore LC, Lowe L. The orthopaedic recognition of child maltreatment. In: Beaty JH, Kasser JR, Skaggs D, Flynn JM, eds. Rockwood and Wilkins’ Fractures in Children. 7th ed. Philadelphia, PA: Lippincott Williams & Wilkins; 2010:192-224.