Talk to the apartment manager face-to-face. Explain your situation. Speaking with someone who can make decisions out of the ordinary can be helpful. Reassure the manager that you have resumes and job applications sent out or that you are receiving some type of steady income. If your situation is the latter, provide proof. According to CriminalHistoryChecks.com, "What is considered acceptable credit history to one apartment's screening criteria/policy may differ from another."
Seek an apartment in a privately-owned complex where managers may be more accessible. Some landlords may base their decisions to rent more on past rental stability than temporary unemployment and bad credit.
Get a letter of recommendation from your last landlord that details your ability to pay on time and be a good tenant. Bring this with you when you meet with apartment managers.
Pay three to six months' rent up front or a higher deposit. Cash can help apartment managers to see green instead of red when you tell them that you have no job and poor credit.
Get a cosigner to sign the lease with you. This person should have good credit and a steady income that could cover the rent in the event that you don't pay.
Rent an apartment with a roommate. Another option is to seek a sublease from someone who must vacate a rental temporarily. You could also rent month-to-month. Your rent likely will be higher than if you sign a year-long lease, however.