The story of Elhanan is not in 2 Samuel 19, but 2 Samuel 21. Servants of David killed the remaining 4 brothers of Goliath. David took 5 stones to the original fight with Goliath but by the time of the confrontation with the remaining brothers he was King and his men counted him too important to Israel to be risked in battle.

15 Moreover the Philistines had yet war again with Israel; and David went down, and his servants with him, and fought against the Philistines: and David waxed faint. 16 And Ishbibenob, which was of the sons of the giant, the weight of whose spear weighed three hundred shekels of brass in weight, he being girded with a new sword, thought to have slain David. 17 But Abishai the son of Zeruiah succoured him, and smote the Philistine, and killed him. Then the men of David sware unto him, saying, Thou shalt go no more out with us to battle, that thou quench not the light of Israel. 18 And it came to pass after this, that there was again a battle with the Philistines at Gob: then Sibbechai the Hushathite slew Saph, which was of the sons of the giant. 19 And there was again a battle in Gob with the Philistines, where Elhanan the son of Jaareoregim, a Bethlehemite, slew the brother of Goliath the Gittite, the staff of whose spear was like a weaver's beam. 20 And there was yet a battle in Gath, where was a man of great stature, that had on every hand six fingers, and on every foot six toes, four and twenty in number; and he also was born to the giant. 21 And when he defied Israel, Jonathan the son of Shimea the brother of David slew him. 22 These four were born to the giant in Gath, and fell by the hand of David, and by the hand of his servants. 2 SAMUEL CHAPTER 21 KJV