Your scenario breaks down here. No way to be "conservative" and funny. People's exhibit A: Blue Collar Comedy.
Hyuck hyuck.
I know this is mainly a joke, but I disagree and prompted this rant you're now going to have to endure from me.
Adam Carolla is one of the greats IMO.
Dennis Miller, Nick DiPaulo, Artie Lange are up there as well.
Joe Rogan, Jim Norton, Bill Burr are libertarians who are greats in their own right.
Trey Parker & Matt Stone are, as a duo, two of the greatest comedic minds to have ever lived, IMO.
There are X'ers who will fight you if you imply Vince Vaughn is not and has never been funny.
Adam Sandler has put out a lot of mainstream slop lately, but in the 90s it didn't get more simultaneously irreverent and popular than him in comedy.
Tim Allen...
Ok, I should probably stop while I'm sort of ahead.
The list gets bigger and bigger depending on how you define "conservative". Increasingly it means being edgy, politically incorrect, and adamantly pro-free speech. The list of comedians that have vocally spoken out against left-wing politically correct censorship includes just about every single comedian I consider funny.
Edgy and dark humor are slowly becoming taboo and being replaced by smugly pontificating leftist politics into a camera. Jon Stewart started it, and IMO did it well. It was somewhat original coming from him. Colbert was hilarious as his character. John Oliver is the closest thing after those two to actually somewhat carry the torch of some degree of humor. But even with him, it's much more smug preaching than actual humor. Trevor Noah? Samantha Bee? The comedy has been extremely diluted by the time we got down to them.
/rant