The phrase "a source of unending" is correct and usable in written English.
It can be used to describe something that continuously provides or generates a particular quality or resource without limit.
Example: "The library is a source of unending knowledge for those who seek to learn."
Alternatives: "an endless source of" or "a perpetual source of".
She was a source of unending love and inspiration for her closely knit family and friends.
The fact that she was rejected, and believed that this was because of her race, was a source of unending bitterness.
The existence of a Communist base in the Caribbean, therefore, was to be a source of unending vexation for future American presidents.
An artist, gardener, elegant entertainer, fiercely independent and a source of unending comfort for the people she loved whenever they needed solid advice and a sympathetic ear.
That helps to explain why, over the past twenty years or so, it has outperformed most other British cities, in particular its rival Birmingham (my home city, and a source of unending frustration).
It is a source of unending amazement to me that so many celebrities regard an interview as an opportunity to boast about their brilliance, in the belief that this will convince readers they are brilliant.
Soil bacteriologists, during the early 20th century, never fulfilled the promise of supplying a biological source of unending soil fertility.
That is what makes it such a rich source of unending innovation, for the benefit of businesses and individual users alike.
Braced against the icy biting wind, a girl and her arctic fox encounter supernatural wonders as they struggle to find the source of an unending blizzard.
It inspired a made-for-television movie, and became a staple for tabloids and an unending source of interest for true-crime writers, particularly Dominick Dunne.
It's an unending source of fascination, like the religious paintings I discussed a couple of months ago, which entranced viewers for months and even years).
