Devetenáctá sobota v roce je vždy v MÁJI. ??
Not unless you're a 19th century Romantic poet.
I think the only expression where 'máj' is more suitable than 'květen' is 'první máj' (1st of May).
And 'v roce' - does that work?
is ve květnu allowed?
It's not grammatically wrong, but we do not say that. I can't think of a situation where I'd prefer it over "v květnu".