I already addressed this in another thread but very well.
1873 President Ulysses S. Grant (Republican) signed the Comstock Act of 1873 which prohibited contraception, information about contraception, or information about how to obtain contraception from being sent in the United Sates mail or crossing state lines. The law was pushed by Anthony Comstock (Republican) and passed the 43rd United States Congress with little opposition. Both houses of Congress were dominated by Republicans with a 69.9% share of the Senate and a 63.4% share of the House. Approximately 4,000 people faced criminal charges as a result.
Connecticut Governor Charles B. Andrews (Republican) signed into law a complete ban on all contraceptive drugs and devices including a ban on their use by married couples and in regards to private or personal possession, sale, or ownership in 1879. While I can't find information on the party demographics of the Connecticut General Assembly in 1879, the state was a strongly Republican until the 1960s so it's likely that the Republicans held the majority. The law was ruled unconstitutional by the Supreme Court in 1965 (Griswold v. Connecticut).
Birth control for non-married couples was not established until 1975 Baird v. Eisenstadt; a Supreme Court decision which broadened the scope of the Griswold decision and was in regard to a Massachusetts law banning contraception ("Crimes against chastity" (Chapter 272, sections 19- 21A). Whether the crimes against chastity laws were sponsored by Republicans is unknown, but as with Connecticut, Massachusetts was a strong Republican state until FDR and one could reasonably conclude that the laws were passed before then.
USC Law School
Comstock Act (1873) - eNotes.com
Comstock laws - Wikipedia, the free encyclopedia
43rd United States Congress - Wikipedia, the free encyclopedia
Birth Control - A Brief History of Birth Control - Our Bodies Ourselves
General Laws of Massachusetts - Chapter 272 Crimes Against Chastity, Morality, Decency and Good Order. - Section 1 Enticing away a person under 16 for marriage - Massachusetts Attorney Resources - Massachusetts Laws