During his run on Happy Days (1974-84), Anson Williams decided to give it a whirl as a pop singer. As Warren "Potsie" Weber, Williams had covered a number of classic oldies on the show, and so an opportunity was created for him to perform an original number, composed by the series' musical directors, Norman Gimbel & Charles Fox.
I cannot say for sure when "Deeply" was released as a single, but it's clearly aimed at the adult contemporary audience as well as the Top 40. The setting is a graduation ball for Jefferson High, so I'd guess this would be around 1978-9. Funny thing. As much as I'd seen reruns of the series, this is actually the first time I've heard this song.
Edit: 7/19/15: I've since learned this aired originally in February 1977, and "Deeply" was released as a single at the end of the season.