Scour yard and estate sales. People will often sell children's books from home as opposed to taking them to book stores. Look for signs of upcoming sales around your neighborhood or in your local newspaper or circular. The other benefit of this method is that you will often be able to negotiate a good deal for the books.
Visit a used bookstore. This may be one of your best options as used bookstores are, of course, loaded with inventory and sometimes have dedicated sections for children's books. If you have a relationship with a bookseller, you can often put in a request for the children's book that you are trying to locate. In addition, you can also often negotiate a price with a used book merchant.
Talk to friends and family who you know had 1970s children's books at some point in the past. You may be surprised at what others have lying around the house or garage, and how many are happy to free up space in their homes.
Utilize an online service that specializes in locating used and hard-to-find books. Sites such as these are a clearinghouse for booksellers all over the country and around the world. In general, locating a book can be as quick as entering the title or the author in a search engine and then locating a price you can afford.