Ah yes character voices where dreams of sounding like a professional thespian come to die. I find that going for a more general tone and inflection works better than trying to be a specific voice.
For example when I play a lizard folk I go for a harsh raspy voice kind of like a ghoul from fallout. When I play my female dragonborn paladin I try not to do a girl voice so much as give her a lighter tone and inflection that reflect her noble background. I do have some exceptions like my rogue who literally talks like the most stereotypical pirate you can imagine
... In hindsight, most of my characters have some kind of distinctive accent/voice pattern, for better or for worse and with varying degrees of intentionality. Obviously I won't go into every single one, but just to illustrate the spectrum:
My Vanara Gunslinger's Western accent just kind of came about because it seemed obvious and because I thought it'd make for a funny joke of "you were raised by elves, why are you talking like this?"
My Fairy Oracle originally just had a higher pitch, and then somewhere along the line after playing she just kind of fell into a German accent and it stuck.
And then there's my Cleric of Asmodeus, whose voice was half the entire initial concept, because the idea of a perfectly well-meaning (if still a little manipulative) lawyer cleric occasionally lapsing into screaming "ALL GLORY TO THE ARCHFIEND!" in a southern accent like a bad televangelist gave me the giggles. And while I'll give 5E a lot of flak, it did make playing a Lawful Good Asmodeus Cleric a bit easier than it would have been in Pathfinder.
I feel like the worst part of writing an accent is what to do with a word that, by all rights, shouldn't really have any phonetic changes as far as I can tell but should still probably sound funny (see: Hoboken).
I want to say the answer is "listening to a table full of players ALL doing accents"?
I'm laughing at myself because - guilty as charged - I also doing accents in our tabletop. Very poorly. Once I tried to do French accent and everyone was convinced it was Latvian. Since then I try to mostly just do voices.
(The answer is "reading an accent". It looks so weird.)
Author Notes:
Or turn them into a punchline. Either or.