For live action only.

I like Scary Movie 2, Clerks 2, and both Austin Powers sequels are better I think.

Deadpools seem about even to me, otherwise no modern candidates without breakout comedies to make one with. Anchorman 2 was decent.

Austin Powers 2 comes to mind for me too, other than that it feels like slim pickings.

I also feel tempted to say a Police Academy sequel, because I loved all of them before, but now I haven't seen any of them for ages and no clue on my feeling about it now.

Well there are some solid ones, even if there aren't necessarily as funny as the original. Then there are movies like Evil Dead 2 and Gremlins 2 that are obviously funnier than the predecessor. This might be an underrated pick but I think The Muppets series is probably the best comedy franchise ever for everyone (All the films are pretty great in their own way) I'm gonna ignore animated films. Also Bad Boys II, Lethal Weapon 4, and Die Hard with a Vengeance are great additions to the series because they are so dam funny.

Ones I actually think are better:

Addams Family Values
Hot Shots: Part Deux
National Lampoons Christmas Vacation is absolutely better than European, and many argue is better than 1.
A Very Brady Sequel
Grown Ups 2 ( I thought the first was meh, but found the second to be almost batshit crazy where so much landed for me)


Other Great ones that are equally enjoyable:

Naked Gun 2
22 Jump Street
Austin Powers 2 and 3
Father of The Bride Part II
Clerks 2
Harold and Kumar 2
Waynes World 2
D2: The Mighty Ducks
Meet the Fockers
Bill and Ted
Grumpier Old Men

Ones I have no problem with but are inferior
Beverly Hills Cop 2, Home Alone 2, Ghostbusters II, City Slickers II, Crocodile Dundee II, Ace Venture: When Nature Calls, American Pie 2 and Wedding, Rush Hour 2, Naked Gun 3.

I can't think of anything else at the moment. There were a lot more decent comedy sequels thinking about it.