You might be able to almost completely cover the cost of a new air conditioning unit through private and government grants. The rating of the air conditioner should guide your choose for a new unit, because energy efficient units usually qualify for more credits. At the very least, a new A/C unit is a wise choice for your utility bill, so financing a new A/C might save you money.
In 2009, the federal government appropriated $300 million to the states as part of a economic recovery package. The State Energy-Efficient Appliance Rebate Program usually includes air conditioners, although the states can set their own standards for what appliances count toward SEEARP. Generally, you have to buy an A/C unit that meets EnergyStar standards -- it will have the EnergyStar seal -- although some states, such as California, require efficiency standards above that of EnergyStar. If you want a SEEARP grant, apply fast, because the states award grants on a first-come, first-served basis.
FurnaceCompare.com suggests contacting local charitable organizations about grants for an A/C. Nonprofits tend to help with emergencies, such as when you have no A/C during a heatwave, but it does not hurt to ask anyway. Modest Needs, for instance, is a charity that awards $1,000 grants for emergencies, which might include fixing a broken A/C unit. You also could ask the United States Department of Health and Human Services' Low Income Home Energy Assistance Program for help locating financial assistance for buying or fixing an A/C unit.
Federal Tax Credit
An A/C unit that qualifies for the SEEARP grant probably also qualifies for the energy efficiency tax credit. In 2011, you can take a $300 dollar for dollar deduction for buying an EnergyStar-approved A/C unit. However, not all EnergyStar units qualify for this tax break. The A/C unit must have minimum seasonal energy efficiency ratio (SEER) -- a ratio based on the amount of energy needed to bring the house down one temperature degree -- of 14. Units manufactured before 2006, for example, could have a SEER rating of 10 and still qualify for the EnergyStar seal, but would not qualify for the tax credit.
When charities cannot offer help to get you an A/C unit, consider thumbing through classifieds for people that might trade an unneeded A/C unit for help, such as watching pets or house cleaning. You could apply for an energy efficiency loan. The Federal Housing Administration, for instance, offers loans for improve home energy efficiency by refinancing your mortgage and adding the cost of a new A/C into your loan note.