Unfortunately, I've never had any luck -- until last week. And believe me, when it rains it pours.
Through three different avenues in less than five days, I was able to come up with three of the character figures from the Neighborhood of Make-Believe Playset and one from the Musical Trolley which was made by the same company that year. One person was looking to get rid of the Daniel Tiger figure which came with the Musical Trolley while another had Henrietta Pussycat and Prince Tuesday from the NOM Playset. As if that wasn't enough, just a few days later, I came across someone with the King Friday figure from the playset.
First, let's look at King Friday. In fantastic condition aside from a minor nick in his mustache, King Friday is marked on his underside with © F.R. 1954-77.
Prince Tuesday is missing a bit more paint, mostly from the inner part of his left arm and the base of his legs. Prince Tuesday is marked © F.R. 1975-77.
Henrietta Pussycat is in the worst shape of the four pieces I found. With a significant amount paint missing from her face, she is otherwise in pretty good condition. Henrietta is marked © F.R. 1956-77.
Last but not least, Daniel Striped Tiger comes from the Ideal Musical Trolley. This figure was included with the Trolley along with a figure of Lady Elaine Fairchilde. Daniel is marked © F.R. 1954-77
Although I am beyond excited to have found these four pieces, my desire to find the others has now intensified exponentially. At the rate of three or four pieces every few years, I might have an entire set by the time I retire.
Of course, if you have any pieces of this set or know where I might find some, please let me know!