We live in the state of Michigan and had a stillbirth back in October. Are there any tax credits for this unfortunate circumstance? What would we need to provide?

No.  Per the IRS, you may not claim a stillborn child as a dependent.

https://www.irs.gov/faqs/filing-requirements-status-dependents/dependents/dependents-10#:~:text=In%20order%20to%20claim%20a,stillborn%20child%20as%20a%20dependent.

The state of MI takes a different stand on this :  

In 2018, Michigan passed a law to allow parents to claim their stillborn child as a one-time dependent on their taxes. This assistance is meant to offset medical and funeral expenses to grieving parents; a child who dies a day before birth should be treated the same as a child who dies a day after birth. The House and Senate votes on those bills were unanimous.

The legislation passed on Tuesday will waive the fee for a certificate of stillbirth. The certificate is needed to claim the stillborn child as a dependent.

Of course, @Critter-3 's answer applies only to your Michigan state tax return, not to your federal return.