Using a simple Google search, you could easily find links to several pieces of modern poetry about the above subjects by using keywords [poetry] + [subject] + [poverty] or [alcoholism], but I'm not sure you are looking for just any poem.
For poetry on the subject of poverty, you could look at many of the poets from the Harlem Renaissance as well as modern African American poetry. Poets like Langston Hughes of the Harlem Renaissance, and Maya Angelou, of today, often wrote about the oppression they (and others) faced as a result of poverty and racial inequality. Much of their work is about overcoming the hardships of their background. Another book that might be of interest to you is called The Rose that Grew from Concrete, by Tupac Shakur. It is a collection of poetry that he wrote before he became famous and many of these poems deal with the struggle of poverty and racism.
As for alcoholism, the first poem that comes to my mind is "My Papa's Waltz" (Roethke) which most interpret as a glimpse into the evening of a young boy with an alcoholic father. Some other older poems that simply deal with alcohol or drinking in general include:
- "Ode to a Wine Jar" by Horace
- "John Barleycorn: a Ballad" by Robert Burns
- "I Would to Heaven that I Were So Much Clay" by George Gordon, Lord Byron.
Up & Out, by Nila Northsun is also a good one, as is Harlem, Montana, Just Off the Reservation, by James Welch.