EA2-5TNU from Kemet/Yageo. 28mA coil current. ATTiny absolute max current per port is 40mA, and I feel 28mA is far enough to be safe. It's also just a short pulse to latch the relay, not a continuous load, so there's no overheating. I haven't had any field failures.
Come to think of it, the relay coil won't see a full 5V from the attiny. There will be some voltage drop on the output pin due to the 178 ohm or so coil resistance loading it. So if it sees, say, 4V, it will only draw 22mA. It's guaranteed to latch reliably down to a minimum of 3.75V.
Don't show this to an EE. He'll blow a fuse