If the LLC made the donation, you can't take an additional write-off. You will deduct the purchase price as a business expense, and you will not book any corresponding revenue—that reduces your taxable profit already, and you can't take a further deduction.
There are slightly different rules if the item was inventory that you purchased in a previous year (and deducted as a business expense in the previous year). See publication 526 under "donation of inventory."
https://www.irs.gov/pub/irs-pdf/p526.pdf
If a church meets the legal requirement for tax exemption under 501(c)(3), they are considered exempt and may receive tax-deductible donations, even if they have not formally registered with the IRS. You may also find that if a local church is part of a nationwide denomination, the nationwide church may have a tax-exempt registration that covers their local churches. However in this case, this issue is moot because you can't take any special deduction for the equipment beyond your normal cost of goods sold.
Finally, I would ask you to be aware that if you are using LLC funds for personal expenses, the other partner(s) could consider this misappropriation of funds (although that is not strictly a tax matter). Hopefully your partner was in agreement with this donation.
