appear, brim in your eyes, brim over, come, fill your eyes, form, gather, spring into/to your eyes, start, well (up)
When she heard the sad news, tears started rolling down her face.
course/pour/roll/run/slide/trickle down sth, drip into/onto sth, fall, flow, overflow, stream
When she heard the sad news, tears started streaming down her face.
stand
Tears stood in her eyes as she read the letter from her old friend.
blur sth, cloud sth
Her tears clouded the bathroom mirror as she tried to see her reflection.
burn (sth), prick (at/in) sth, sting your eyes
Hot smoke made tears burn his eyes as he rushed out of the kitchen.