It's unlikely you will mitigate W-2 earnings as passive income (rental activity) won't reduce your w-2 income tax liability.
As for replacing the AC. If you are replacing a broken AC I suppose it would be classified as as a repair rather than a capital improvement. It's deductible in the current tax year but I'm going to guess your tax deduction from the AC replacement will make your passive income net negative for the 2016 tax year and you'll carry forward the loss to next year.
@Edwin Rodriguez , You can mitigate your W-2 income via losses from a passive activity, rental loss. The general is a rule allowing up to $25,000 of active participation(see below) rental real estate losses as a deduction against nonpassive income.
You will be deemed to be actively participating if you make management decisions in a significant and bona fide sense. Management decisions that are relevant in determining whether you actively participate include approving new tenants, deciding on rental terms, approving capital or repair expenditures, and other similar decisions.
There is a phase out if your MAGI is above $100,000.
So, if you increase your expenses via repairs to the rental property, you might be able to use that passive loss to offset your W-2 salary this year and also going forward.
If your "air conditioner" is a window unit, then replacing the unit is the same as providing personal property for the tenant's use. If you choose to depreciate, it has a five year class life. On the other had, if you are really talking about an HVAC or central air system, then the cost is likely far in excess of any de minimis rule and you will end up depreciating. In either case, you will spend much more money than you will save on your taxes.
To the greatest extent possible, you want to pay for repairs out of your cash flow, not out of your pocket. In effect, the tenant is paying for reapirs, and at the same time, the repair cost lowers your taxable rental income.