Would've recommended a Infinity Kappa Perfect 12 but since they're not available the closest thing you can get is a Infinity Reference 1262w i've tried it in my car and it's not as good as the perfect 12 but it comes close,you can get the box and the sub in your budget.
1.25 cubic feet 0.75 inch sealed MDF box with carpet should get the job done.
p.s 1262 is available,let me know if you intend to know where to get it from.