Where can I find the 1960s New Math syllabus?

Perhaps the primary source would be the documents created by the School Mathematics Study Group.

[...] the School Mathematics Study Group (SMSG) created and implemented a primary and secondary school curriculum between 1958 and 1977 that was widely known as the "new math."

Some films made by the group are found here.

(For context surrounding the "New Math" reform, see "A Brief History of American K-12 Mathematics Education in the 20th Century" by David Klein.)

The book, The New Mathematics Made Simple by Kempf and Murphy, is available online in PDF format. It should give you a pretty good grasp of what was being taught back then.