Cat rehoming advice

Tough post to be making but looking to rehome my late grandmothers cat. Our family took her in after my grandma passed but cannot commit to taking care of her unfortunately due to work travel and other commitments. We have asked around many friends and colleagues and there seem to be no takers. I keep hearing that all shelters are at capacity and I absolutely do not want to put her in a kill shelter god forbid. Does anyone have any advice or tips?

She’s 4, perfectly healthy, vaccinated, spayed.