Okay I really don't know where to look from here, so can we try to compile a list of the most logical interpretations of the riddle. (I'll edit it if you have suggestions or I think of more)
The regular bearer appears irregularly if you know where to look.
(in no particular order)
1. Zipper
"Regular bearer" meaning Zipper bearing eggs
"appears irregularly" meaning April Fools Day/ Halloweaster
2. Megan
"Regular bearer" meaning Megan the "normal" bear
"appears irregularly" meaning hard to find/new villager/no amiibo/mystery islands
3. Mango Trees
"Regular bearer" meaning Mango (Alphonso) Trees
"appears irregularly" meaning irregularly bearing fruit
4. Redd
"Regular bearer" meaning regularly brings art to island
"appears irregularly" meaning in plaza during fireworks festival
5. Jeremy/ moderator
"Regular bearer" meaning bearer of news, announcements, collectibles/currencies
"appears irregularly" meaning posting somewhere they normally don't/ looking different than normal
6.
"Regular bearer" meaning
"appears irregularly" meaning