So I can't find a lot about Arizona and African American attitudes during your time, but I found some unique histories.
During the Civil War, a portions of the New Mexico territory (including present day NM and AZ) petitioned the Confederacy to join but this was mostly because mail service was cut during the period and the region felt that the CSA could better deliver. A few small battles occured in the state, including a three way battle between the Union, Confederacy, and Native Americans, but the territory was held by the Union after the dust had settled.
From there, AZ (now it's own territory, split in part to limit it's ability to join the Confederacy again) was basically your standard Western setting. Contrary to just about every Western movie you've ever seen that wasn't made by Mel Brooks, African Americans represented something between 15% to 25% of employed Cowboys in the U.S. Many were drawn to the profession as the west wasn't nearly as discriminatory as the rest of the United States, and the hazardous nature of the work further lowered that as loyalty, individualism, and honor were valued, skin color be damned.
This may explain Arizona's high African American population relative to it's location in the U.S. in 1900 it was the western most territory of the United States with an African American Population above 1% of the population, and by 2010 that demographic changed to about 4%. During this time period, on they Coastal West and Nevada would see larger growth of populations by percent than Arizona, which was some of the highest in in that period. It's important to understand, that 1900s was the start of what is known as the Great Migrations in African American History. The first Great Migration lasted from ~1910 to 1930 and saw the movement of 1.3 million African Americans from the former Confederate States to just about anywhere that wasn't the South. The depression brought this movement to an end but by 1940 it was back in force and another 5 million moved to anywhere that wasn't the South.
The 1930s would also see the beginning of a rise to fame for an important African American leader Eddie Anderson. In 1937, Anderson was hired by Jack Benny to play a one time role of an African American Train Porter who would get the better of Benny in their interactions. The jokes were so loved, that five weeks later, Anderson was brought back on to play a waiter and would get the better of Benny. Anderson would receive one more one time role on the Jack Benny Program before the fan demand was such that Benny would hire Anderson full time to play the character of Jack Benny's valet and good friend, Rochester van Jones. He was the first African American Actor to be a regular actor on a nationally broadcast program.
The popularity of the character was a hit with audiences and was the most popular character on the Jack Benny Program, next to Benny himself. In one early incident, Anderson was seconds late to a train taking to production crew on tour, but was able to get an LAPD motorcycle escort out ran the train to the next stop, where he boarded. By 1940 (three years after Anderson's debut), Anderson was invited to visit Harvard University by the Students, only to be intercepted at the airport by rival MIT students, pretending to be the Harvard Students... when the Harvard Students discovered prank, they literally rioted against the MIT students.
Much of Rochester's early character was very much racial stereotyped early on, but Benny always made it clear the both Anderson's character and Anderson himself was an honest and valued friend of his. Twice, while touring in the South, when hotel owners refused to give Anderson a room, Benny would threaten to to take his business elsewhere. In the one instance that Anderson was rejected after the threat was issue, Benny followed through... as did all 44 cast and crew. Anderson was one of the highest earning actors in the industry at the time, earning a Salary of $100,000 (for a comparison, the stars of the competitor program Amos and Andy were given a collective salary of $100,000, which they split three ways with the show's announcer). Following the War, and the news of the full extent of the Holocaust, Benny worked to remove most of the racist elements of the character's humor. The last vestiges of racial humor were Rochester's alcoholism and gambling and laziness in work, which by this point in the show, were attributes of Rochester because that was just who Rochester was as a person, than attributes of Rochester because he was Black... in fact, most of the humor surrounding the character's laziness was his ability to trick Benny's character into doing the work (The humor of Rochester being underpaid for his job was also not a racial componant... one of running gags was that Benny was a cheap man, to the point that one of the funniest jokes in the entire show's run on the shows run occurred a mugger gives him the choice of "Your money or your life?". Benny pauses and the mugger repeats the threat, only for Benny to quip right back "I'm thinking it over!").
Suffice to say, given that murders happen but not on screen and you are expecting the audience to be mature enough to know that racism was a thing in the 30s, perhaps treat it the same way. Don't overtly show racism... but have the characters who would act like racists say things that are definately racist, but not overtly. Consider the Bankers and how they talked to Tiana in Disney's Princess and the Frog (the movie was set in the 1920s in New Orleans.) or the seen from the Teen Titans where Cyborg discusses with Starfire how he's very much aware that it hurts when people can judge you based on what they see on the outside and he understands how upset she is over having to work with a racist alien, and Starfire immediately concludes that Cyborg is talking about how people judge him because he is part machine. It's pretty clear that he was hinting at the fact that he's African American, but decides not to correct the record and just teach the lesson. If you actually want to be more overt, look up Disney's short cartoon John Henry, which explicitly stated John was born into slavery, but wouldn't let that keep him down, and most of the (White) rail workers accepted John in the post-civil war setting.
I could easily see this character as being a very unique example of an African American Cowboy who learned from his father or grandfather (depending on age), a man who valued his freedom from slavery. I'd also give him a sort of whit and a strong individualism streak that makes him well aware of the state of racial politics in the era, but also allows him to always get the better of anyone who thinks they are better than he is. Anyone who underestimates this guy will do so at their own peril.