They are both fine but have completely different meanings.
On Sunday morning(s), I run in the park. (This describes something you do in the past, present and plan to do in the future. The ‘s’ is optional. No ‘s’ is the most general and categorical, suggesting you almost always do it. With an ‘s’ it is still a general habit but, imprecisely, perhaps not quite as consistent.)
On Sunday morning, I ran in the park. (Once in the past. The default meaning would be last Sunday. However, if the context were that you were talking about a specific week in the past, it would mean Sunday of that week.)