128 bit AES CBC bit flipping on second block
There is only one way I see how to avoid having this block of garbage in you plaintext after CBC bit flipping attack, but it requires to be able to see the result of the decryption and to know the whole plaintext you are attacking, which may not be the case in most practical scenarios.

Say you want to alter the third block of plaintext, P3:


Do your CBC bit flipping attack on P3 by modifying C2, the normal way
get the modified plaintext. P2 should be garbage
now modify C1 in order to “repair” P2, that is, C1 = (the garbage you got) XOR (the original P2)
this is going to mess up P1, so you now you modify the IV to “repair” P1