Can limericks be dark?

I am studying poetic forms.

http://www.criticalreading.com/poetry.htm

In general  the limerick is a humorous form.That is,both historically and by the shape and brevity.Yet I am trying to write some miserable limericks.I am finding it harder than I expected.The first one certainly has come out with more than a hint of fun

AS BROAD AS IT’S WIDE

I once had therapeutic depression

The counsellor wept through my session

So I gave my advice

As broad as it’s wise.

Depression sure beats going fishin’

ANXIOUS

I feel very anxious today

Would I do better to worry or to pray?

I’ll trust in the dark

Tn the bush by the park.

Till a man comes along feeling gay.

I see the very nature of the form almost makes it compulsory to be funny.It’s lines 4 and 5 I think

 

 

NEW FRIEND

I hate my new  man friend already

I thought he would make me more steady

But I feel giddy and sick

When he gives me a lick.

Such a  dog’s not ideal for a lady.