What is the term for the kind of laugh that Ernie makes on Sesame Street?

Solution 1:

I would call that a "fricative laugh." In phonology and linguistics, "fricative" describes any sound generated by voicelessly pushing air through a narrow space.

Solution 2:

I would call Ernie's laugh a "cackle." While a cackle has associations with evil characters, Ernie is more mischievous than evil.

That laugh I would write as "Heh heh heh."

Solution 3:

Consider calling the fricative laughter a "snicker". It can be contrasted with the overt gaffaw.

snicker noun 1 A half-suppressed, typically scornful laugh; a snigger. ‘he could not evoke a snicker with his jokes’ - ODO

Although the term can carry derisory overtones as noted in the definition, in conversational usage it is appropriate for Ernie's mischievous laughter.