At least 31mm of Xmax is going to be the killer. Most of the popular under $300 SPL subs (AB TNT/Elite, Sundown SA, SSA ICON, Incriminator lethal injection, DC level 3) are going to have way less than 31mm Xmax.
Something like the soundqubed HDX3 will meet the requirement price/Xmax wise but I hope you plan on dropping around $800 on electrical upgrades or else you won't barely get a pair of those subs moving.
If your not planning on going all out with electrical your budget/Xmax requirement might be better suited for a single 12 or 15 but higher price ($500-600 single 12 or 15 but higher tier)