Here's what rhymes with stabilises.

Consider these alternatives

stabilizes / prices deteriorates / states worsens / persons reassessed / best abates / states stabilise / price subsides / rights escalates / states disintegrates / states materialises / serialises destabilizes / prices recedes / needs decelerates / states materializes / enterprises reevaluated / dated consolidates / states outgrows / those degrades / states equilibrate / late deteriorate / late falters / orders