I don't think that you will find any film from the 1960's which is still available which is anything like it was then. The two main types of color negative at that time were the Kodacolor-type and the Agfacolor-type, both of which used different basic color couplers and processing procedures. There were similar products from smaller makers, particularly the European manufacturers, which based their film on Agfa information released after WW2.
However, present C-41 films from Kodak and Fuji use a different process from those in the 60's, whereas the Agfa process is effectively obsolete.
Unless you were to take the complicated way of actually finding old film from that time, then some way of formulating the process chemicals (not impossible, but not easy, and rather unreliable), I think that Tom's suggestion of a near-match from a modern film and post-post processing should work. I've seen quite a few examples in magazines, and even digital video processed to look like old Kodachrome home movies!