Use a sterile saline respiratory ampule: wet the fluorescein strip with the saline, squeeze out half of the saline, then suck the yellow fluorescein liquid back up into the ampule. Now you can use the ampule as an eyedropper. For uncooperative kids, lay them supine and squeeze the liquid into the medial corner of the closed eye - when they open their eyes it will run into the eye.
(Amazon.com)
For additional methods, see AliEM's great tricks of the trade post at:
https://www.aliem.com/2015/tricks-of-the-trade-fluorescein-eye/