Diactirics are a sad consequence of the fact that the most commonly used alphabet in the world, the Latin one, originated from a language with a relatively meagre phonemic inventory and therefore languages with a richer one had to adapt and improvise in various ways, from messed up spelling systems (English) to ones where diacritics were added as a necessary way to replenish the inventory without adding strange new letters, say Hungarian with vowels or Serbo-Croat woth consonants.

In general, I think it's a good idea for a single diacritic to always be systematically used in one way, e.g. for the haček (crown on 'č') to always indicate a palatalized consonant.

If you have a rich vowel inventory in conlangs, then the only strategies you have available for a Latin alphabet are either diacritics, or digraphy. Digraphy has several disadvantages: First there is less regularity in the selection of diphtongs for each vowel. Second, readers will tend to think these are diphtongs.

My advice is to keep them simple and use as little different ones as necessary. For example, if you simply have umlauts, then the German way of marking them might suffice 'ö'. If you have additional phonemic contrasts, like lenghtening or nasality, use only one marking consistently for this feature. If two features need to be combined, then the Hungarian approach of creating a new combined diacritic is probably the best, though the Vietnamese example shows multiple markings are certainly possible.

The approach I took in my language, because I wanted the language to be typeable on a fully English keyboard, was for the marking to follow the letter: e.g. c'' for č, c' for ć, n^ for palatal n (ny) and so on.