Ahh, yes. That tender two-person configuration known as the hizamakura (lap pillow) which can denote a parent-child relationship or something more romantic with a young couple. Of course, the intimacy and awkwardness are squeezed for all they are worth in a lot of anime. For that matter, this can lead to another trope: ear-cleaning but since I've yet to find a kayo about that custom, I'll just go with the hizamakura for tonight.
I was able to find one with that exact title. "Hizamakura" was a single by kayo singer Michiko Maki（牧美智子）released in May 1974. The song was written by Kazuya Senke（千家和也）and composed by Daisuke Inoue（井上大輔）when he was still going by his real name, Tadao Inoue（井上忠夫）, a few years after he had left his old Group Sounds band, Jackey Yoshikawa & His Blue Comets（ジャッキー吉川とブルー・コメッツ）.
Unfortunately enough, I couldn't find the lyrics to "Hizamakura" online but from what I could hear from Maki herself, it seems as if her protagonist is perhaps enjoying her beau sleeping softly in her lap and wondering what the future portends for them. The music is suitably innocent but also has that sense of uncertainty. For the singer, this was not only her first single under the CBS/Sony banner but also her first single under the stage name Michiko Maki. In terms of her entire career, "Hizamakura" was her 5th single with the first four singles being released under the name Hiroko or Yoko Aihara（愛原洋子）.