The acquisition date for certain mutual funds is not shown on the 1099-B, Box 1b. The purchase date was over 30 years ago. What do I enter for purchase date?

If you know the approximate Date Acquired, enter that date if your 1099-B is blank, and supporting documentation has no info. 

Anything acquired over one year ago is considered Long-Term. 

Click this link for more info on Date Acquired.

If the idea of being off +/- two, +/- three or even +/- five years bothers you, enter "various". 
as mentioned, if it is acquired over a year before date sold, it is Long Term.