Citizens of the United States only require a government identification and a proof of citizenship (or a document that is both, e.g. a passport, passport card, enhanced driving licence, or NEXUS card) to enter Canada.
Technically there is no requirement for photo identification, but the officers can refuse entry if there is doubt to if a non-photo ID in fact belongs to you. For minors travelling with their parents (who have photo IDs) and the parental relationship can be established (same last names or information on birth certificate), photo IDs are in practice not necessary (but may still be helpful, even if expired).
Note that for air travel, the airlines are required to demand a passport or NEXUS card.
This used to be explicit on the government website but nowadays the information can only be inferred (probably because the Canadian government would prefer you to have a proper travel document such as passport).
The requirement for a valid passport or travel document is provided by section 52 of the Immigration and Refugee Protection Regulations. Subsection 52(2) contains exemptions to such requirement, including for citizens of the United States
52 (1) In addition to the other requirements of these Regulations, a foreign national seeking to become a temporary resident must hold one of the following documents that is valid for the period authorized for their stay: (a) a passport [...]
(2) Subsection (1) does not apply to (a) citizens of the United States; [...]
The exceptions are also discussed in the IRCC/CBSA operational manual ENF 4: Port of entry examinations (section 13.16).