on TV during the time Beaver was on?

Where they similar to Beaver? Did mom stay home and dad go to work? Were they supposed to be funny etc...

The Andy Griffith Show

Aunt Bee stayed home and Andy went to work.

You had Make Room for Daddy/The Danny Thomas Show, which began before and ended after Leave It to Beaver. Sitcom, dad went to work but he was in show business so he was usually around during the day. The first mom quit after a couple years - instead of just replacing her in the role they went thrrough a couple of years of finding and hiring a nanny, turning her into a wife, then erasing any sign that it was a blended family.

How about "The Real McCoys" 1957-1963?

It's kind of a hoot watching that show keeping in mind some of Richard Crenna's later roles.

Father Knows Best, The Adventures of Ozzie and Harriet, My Three Sons (no mom, but Bub and Uncle Charlie stayed home).

Were they similar to Beaver?

To give an opinion on this question, Beaver was unique in its time. No other shows had scripts which were centered only on the lives of the kids.

Yes, Jay North was credited as the star of Dennis the Menace, and many stories were about his doings. But others centered on happenings with the adults, with which/whom he interacted.

In other sitcoms of that era, the kids were relatively important to the show, and had their fair share of stories. Father Knows Best and My Three Sons, for example. The Donna Reed Show and The Dick Van Dyke Show, not so much (see titles).