I've never fired a 3" 20g but believe there's likely a good use for them. But it's more appropriate in a gun like a BSS or Citori, both of which typically weigh around 7lbs, or an 1100 Rem, than in a little flyweight sxs.

If Experience is just looking for killing coyotes or turkeys as a 'target of opportunity' during other hunting with the Bernie, that's one thing. But to specifically go after 'yotes with a scattergun is a tough task and requires a heck of a lot of stealth effort to get that close to 'wiley coyote'(why do you think they call them that?). We're talking bow ranges here. Take a look at this guy's techniques if you're serious.
http://www.varmintal.com/ahunt.htm