If not actual "Little League" baseball (the corporate entity and trademarked brand name) then there is probably plenty of "youth baseball" in your area. PONY, USSSA, Babe Ruth and Cal Ripken leagues are all over the country- none of which have any affiliation with "Little League Baseball, Incorporated".
There may even be "independent", community-based leagues in your area that run their own umpire programs- and you might not even need to have any sort of certification to umpire those, especially for the younger age groups.
Use your phone book, the internet, Google, whatever to search out as many youth sports associations, leagues or teams in your area. Usually they are dying to find people to umpire games. Also search out and contact any umpire associations around you- they are should be able to provide you with contact information for leagues needing umpires, and possibly even assign games for you.
If you really want to umpire, now is the time to start looking into it. Be proactive. The key is to contact as many people as you can, get your name out there and get as much information as you can now, before the season gets into full swing in a couple of months.