I guess I am in the minority but I kinda like it!! I
McCoy [name_m]William[/name_m] McKinney sounds like a pretty strong name !
If you are feeling discouraged would you and your partner consider switching the middle and first name ? [name_m]William[/name_m] McCoy McKinney And than using the middle as the name you call him but have that “formal first”
Other suggestions
[name_u]Corey[/name_u] McKinney
[name_u]Connor[/name_u] Mckinney
I like [name_m]William[/name_m] McCoy McKinney a lot, way more than McCoy [name_m]William[/name_m] McKinney.
William McKinney makes me think of [name_f]Christina[/name_f]’s son from Ugly [name_f]Betty[/name_f]. Positive association though because [name_f]Christina[/name_f] was my favorite character. 
Is Macoy McKinney any better?
Yes, Macoy is better. Maybe still not ideal, but it could definitely work.
Personally, I like the distinctive sound of McCoy McKinney - he’ll certainly leave a lasting impression on everyone he meets for the entirety of his life!
That said, as a standalone, I don’t particularly like McCoy as a first name. All I can think of is the spelling corrections that he’ll always have to make or specify. Two capital letters in a name sounds like an administrative nightmare (hopefully I’m wrong about this).
I think the McCoy spelling is cuter. If it’s truly your fave - go for it!