Should I report the pronunciation as |ˈˌdaɪəˈˌkrɪdəkəl|, or [ˈˌdaɪəˈˌkrɪdəkəl]?
I think the best way to report pronunciations for the general audience is to use a basic IPA transcription for English and enclose the pronunciations in /slashes/. This matches how dictionaries that use IPA, such as Cambridge and Oxford, mark pronunciations.
I think the other symbols for phonetic transcriptions, like [square brackets] and |pipes| are best left for detailed discussions of phonetics.
The standard convention is
|pipes| are used to distinguish narrow and broad transcriptions (possibly not used in a consistent way by everyone, based on what nohat says). In any case, unless these distinctions are important to the specific answer, then
[brackets] are fine.
As for stress, normally the
ˈ notation refers to primary stress and
ˌ refers to secondary stress (if there is one). So I would transcribe diacritical as:
[ˌdaɪ ə ˈkɹɪ ɾə kəl]
The sound that you transcribed as
[d] is normally transcribed as a flap
[ɾ]. (Also, it is worth noting that, although
[ɹ] is technically the "r" sound of most English dialects, many linguists simply use the symbol
[r] when this distinction is not critical (for convenience); so, feel free to do that.)
Edit: I should mention that using a [d] in place of [ɾ] might be done in a non-IPA transcription — sometimes dictionary pronunciations change around symbols to make it more readable to someone who never learned IPA. But it's not completely accurate.