#beardedkomedy

I’m not sure what you’re getting at, but you might be framing the question oddly. They didn’t exactly do army portraits very often in the 13th century, and images of say, battles they would have been in, would have been extremely stylized and also done significantly later. There are some portraits of important individuals of color, but they’re not “Muslim mercenaries”, or whatever you mean by that?

As far as I know there weren’t any specific military forces under Frederick II that could be classified as such, although to be fair, you have the Fifth Crusade, the Sixth Crusade, excommunication, and the massive campaigns in Italy and Sicily. And as I mentioned, there are images in manuscripts along with descriptions from those campaigns but they were made later:

You have an image from the Nuova Cronica showing Frederick II meeting with Al-Kamil Muhammad Al-Malik, the ruler of Egypt during the Fifth Crusade:

If you’re looking for something more art history rather than military history, this might help:

In the late 12th century positive images of black Africans began to increase in Western art. This phenomenon was encouraged by a developing interest in blacks on the part of the Hohenstaufen emperors Henry VI and Frederick II.

Henry’s conquest of Sicily in the 1190s brought a number of black Moslems under his rule, and miniatures from the period record this fact. In the 1220s his son Frederick established an Islamic colony which included a number of blacks at Lucera in Apulia, and at least two sculptures can be associated with these Africans. One is a capital depicting a remarkably naturalistic black as well as other varied ethnic types.

The second work is evidently a portrait of Johannes Maurus, a black who was Frederick’s chamberlain. The two blacks who appear in the Adoration of the Magi on Nicola Pisano’s Siena pulpit are undoubtedly based on African retainers at the Hohenstaufen court. Even after the fall of the Hohenstaufen, artists made repeated references to the family’s fondness for black people in art and in life.

Black Africans in Hohenstaufen Iconography. Paul H. D. Kaplan. Source: Gesta, Vol. 26, No. 1 (1987), pp. 29-36 Published by: The University of Chicago Press on behalf of the International Center of Medieval Art

Stable URL: http://www.jstor.org/stable/767077 .

Here’s an image of the limestone capital discussed above:

And here are the figures from the Siena pulpit:

[more on the pulpit here]

These are much more likely to be images of Black Christians, however.

You could also check out the book Germany and the Black Diaspora: Points of Contact, 1250-1914  ed. Mischa Honeck, Martin Klimke, Anne Kuhlmann. Page 22 starts with a discussion of the Hohenstaufens.

You might notice in the very first image I posted, the soldiers are wearing the black-eagle-on-yellow standard of the Holy Roman Empire; that of its patron saint, Saint Maurice, whose depiction as a Black man was already traditional by that point.