City of Tacoma and County-wide rent and utility assistance is now available. Visit Pierce County's Rent Assistance webpage to begin the application. You can also call 211 to do the application over the phone.
For some, The Immigrant Relief Fund may be a more attractive option for COVID-19 Emergency Relief. It is not rent assitance, but up to $1,000 is available for those who aren't eligible for federal stimulus funds or unemployment insurance. Apply on-line here or phone 855-289-4503. More details are available here or in Spanish here.
Pierce County put a very informative Rental Assistance Frequently Asked Questions webpage together - well worth the look.