Stamina refills to 100 at daily server reset; recovery speed increases with VIP level and Monarch Talent Lv18. Best free method: Resource Consuming Return Event (needs ~Keep 25+): per resource type, 125M consumed = 100 Stamina x2, 500M = x4, 1,250M = x8, 2,500M = x12, 5,000M = x20; consuming 2,500M across 4 types = 104 pieces of 100-stamina. Otherwise the only relatively good options are Crazy Eggs and Lucky Apples; the rest are small lucky drops. Crazy Egg: smash 6-hammer (James Bowie) egg -> 100 Stamina x4 if lucky. Dwarf's Lucky Apple Blessing (5 wishing coins) -> 100 Stamina x1 if lucky. Free/event sources: Trade Products Event 100x3; King's Path Day2; Login Rewards Lv3 Witch's Treasure Bag; Garuda Trial (10/30/50 kills -> 10/50/100); Lucky Composing boxes; Tavern (25 Stamina x1, 3x/day at 3:30/9:30/12:30 server time); Wheel of Fortune; Arch of Triumph flower rewards. Paid/gem: Shopping Spree, Store, Black Market (50 = 300 gems), Alliance Shop (discount only), packages. For a bot, stamina gates monster/boss hunting (the main free source of speedups, hammers, medals, materials), so top it up daily via the tavern and time Consuming Return events for bulk stamina.
Original research source: Evony Guide Wiki