Just make the limits what they should be and partition them out.
In one dimension you have Integral (a,b) f(x)dx + Integral (c,d) f(x)dx where a=-infinity,d=+infinity and a = -c gives P(|X| > a).
You can apply the same idea except you are working on a two dimensional region instead of a one dimensional one.
If there is no covariance between the two random variables then you will exclude a rectangle at the centre from your probability.
If there is covariance structure, you will need to calculate your limits in a different way depending on the covariance.