Im not sure what your exact experiment is but injection of serum from KBxN mice into B6 is a simple way to induce arthritis. However it is only the effector stage of the disease, not the initiation phase. Search pubmed for Mathis/Benoist and KBxN for this model
Why don't you try Freund complete adjuvant (FCA)? It can induce unilateral chronic rheumatoid arthritis which enables you to use the other limb as control.
Please check this out
doi: 10.1208/s12249-010-9445-5
I know for sure it works with albino mice, but I'm not sure about C57BL/6.
Is there any specificity that you have to induce arthritis only in C57BL/6? If not you can try wistar albino rats for good induction of RA by Freunds complete adjuvant.