Sure. Dialects can vary right down to the particles.
- In Kansai-ben, there is a particle かて which does not appear in standard Japanese. It roughly means 〜ても, でも, さえ etc.
- In Tohoku-ben, the particle さ is used instead of what in standard Japanese would be に or へ: 東京さ行ぐ, etc.
- In some Nagano dialects, を is pronounced /wo/, not /o/.
- In many dialects, including Tokyo dialects, something like 僕は might be realized as /bokaa/ instead of /bokuwa/. I believe that this is more a case of phonetic rules causing this change even when particles are involved, rather than the particle itself having a "different pronunciation," though.
- The sound /u/ in many Okinawan words corresponds to the sound /o/ in the equivalent (cognate) Japanese words, and this applies to particles too: there is a particle /tu/ corresponding to standard Japanese と, etc.
Important note: None of these cases, as far as I know, are the result of the "correct" standard Japanese form being transmitted to a dialect area and then changing there. The dialects grew up alongside standard Japanese, and happened to end up with different pronunciations for some corresponding particles. The difference is subtle but important.
For example, if you were Italian, you might say as shorthand "in Spanish, the word 'il' is pronounced 'el'" (and vice versa if you were Spanish), but it is more accurate to say that a common ancestor word evolved into the words /il/ and /el/ in the two different languages. Neither language is the "correct" or "original" form (if anything, that would be the Latin /ille/, but even this is probably an oversimplification). They are different languages and therefore different words. (They are, however, cognates.)
The Okinawan /tu/ is a particularly good example of this because Okinawan is so distinct from standard Japanese. It's misleading to say "In Okinawa they pronounce と /tu/". It's more like "In Okinawan, there is a particle /tu/ which shares the same proto-Japonic ancestor as (= is cognate to) the particle と in Japanese." But you could say the same about Nagano /wo/, the usage of /sa/ up north, etc. -- they don't derive from modern standard Japanese itself, they come from an older language (or dialect family, if you like) from which modern standard Japanese is also derived.