Typically speaking, a Michigan judgment is valid for ten (10) years and can be renewed if it is not collected in that time period.
MCL 600.5809 provides as follows:
(3) Except as provided in subsection (4), the period of limitations is 10 years for an action founded upon a judgment or decree rendered in a court of record of this state, or in a court of record of the United States or of another state of the United States, from the time of the rendition of the judgment or decree. The period of limitations is 6 years for an action founded upon a judgment or decree rendered in a court not of record of this state, or of another state, from the time of the rendition of the judgment or decree. A judgment entered in the district court of this state before May 25, 1973, is a judgment of a court not of record. A judgment entered in the district court of this state on or after May 25, 1973, except a judgment entered in the small claims division of the district court, is a judgment of a court of record. Within the applicable period of limitations prescribed by this subsection, an action may be brought upon the judgment or decree for a new judgment or decree. The new judgment or decree is subject to this subsection.
(4) For an action to enforce a support order that is enforceable under the support and parenting time enforcement act, Act No. 295 of the Public Acts of 1982, being sections 552.601 to 552.650 of the Michigan Compiled Laws, the period of limitations is 10 years from the date that the last support payment is due under the support order regardless of whether or not the last payment is made.
So long as the time period for appeal has passed, likely 21 days from the date of judgment in your case, you can pursue collection on the judgment. Depending on the method you choose to collect on the judgment you may need to register the judgment in New Jersey if you want to seize property, etc.
While a money judgment in Michigan is valid for a period of ten (10) years (and can be renewed) it sounds as if the judgment-debtor resides in New Jersey. If this is the case, you'll likely need to "domesticate" (move) the Michigan judgment to New Jersey. Since your ex-wife (judgment debtor) resides in New Jersey she likely has no money or property in Michigan.
The process of domesticating a judgment from one state to another is not difficult, however, you will likely need the original Michigan judgment (or a certified copy thereof) for purposes of New Jersey domestication.
Once you have properly domesticated the Michigan judgment to New Jersey you can commence post-judgment collection practice in accordance with applicable New Jersey law.