Will it be hard to get a cosigner for a loan with 500,000 worth of equity?

I owe 200,000 back taxes and the IRS is trying to foreclose my home. I had just had a chapter 7 bankruptcy discharge a week before the IRS filed this foreclosure. Will it be hard for me to get a cosigner now? My wife and I make 70,000 together and have no other debts. My property had just been appraised at 650,000.

There's more to it than the appraised value. It's the appraised value minus what you may owe on it now. If you own the property free and clear and and it's valued at 650K you should be able to get a 200K first mortgage easily. If that's the case, talk to the IRS. If they see you are trying to satisfy the debt they may be willing to hold off until you can get the loan processed.

If the appraised value minus what you owe is less than the debt, it may be more difficult. Most important, talk to the IRS and make sure they know what's going on. They don't want the house, they want the money.