SUNLIN,SŰNLIN

Since the two dots ("umlaut") over the U represent an "E", then an alternative and possibly alternate spelling would be SUENLIN.

“OHG. –lin: sünlin ‘little son’, schtflin; in the modern –lein (scherflein &c.) and in the Swabian –le the effect of the I is obliterated, but in Swiss –li (büebli, füessli &c.) it is still a living force.”
-Selected Writings of Otto Jespersen (Routledge Revivals); Otto Jespersen. Routledge, Mar 17, 2010

For "little son", the modern German is closer to SÖHNLEIN or SOEHNLEIN. In the dialects along the Rhine river, in Wurttemberg and Alsace, the spellings become SÖHNLIN or SOEHNLIN.

So here are some of your choices (minus the spelling errors from Ellis Island and US census takers): SUNLIN, SŰNLIN, SUENLIN, SÖHNLEIN, SOEHNLEIN, SÖHNLIN, SOEHNLIN