You could always move to a Canadian province to give birth. Some provinces allow persons who are neither Canadian citizens nor permanent residents to receive government health insurance for free or at low cost. For example, in British Columbia, government health care coverage is generally available to foreign students, subject to certain conditions. Medical and Health Care Services Regulation, BC Reg 426/97, § 2(a) (authorised by the Medicare Protection Act, RSBC 1996, c 286, § 51). As an added bonus, the child will be a Canadian citizen. Citizenship Act, RSC 1985, c C-29, § 3(1)(a).
Note that you do need to obtain government health insurance before receiving the healthcare; otherwise, you may have to pay out of pocket.