Take a guess as to the rename changes changes needed to the Android part of the build.
I think this should work, but I can't test it.
diff --git a/Makefile.am b/Makefile.am
index 83bacd4..09221a3 100644
--- a/Makefile.am
+++ b/Makefile.am
@@ -74,13 +74,13 @@
 
 Android.mk: Makefile.am
 	androgenizer -:PROJECT json-c \
-		-:SHARED libjson \
+		-:SHARED libjson-c \
 		-:TAGS eng debug \
 		-:REL_TOP $(top_srcdir) -:ABS_TOP $(abs_top_srcdir) \
-		-:SOURCES $(libjson_la_SOURCES) $(nodist_libjson_la_SOURCES) \
-		-:CFLAGS $(DEFS) $(ANDROID_CFLAGS) $(libjson_la_CFLAGS) \
-		-:LDFLAGS $(libjson_la_LDFLAGS) $(libjson_la_LIBADD) \
-		-:HEADER_TARGET json \
-		-:HEADERS $(libjsoninclude_HEADERS) \
+		-:SOURCES $(libjson_c_la_SOURCES) $(nodist_libjson_c_la_SOURCES) \
+		-:CFLAGS $(DEFS) $(ANDROID_CFLAGS) $(libjson_c_la_CFLAGS) \
+		-:LDFLAGS $(libjson_c_la_LDFLAGS) $(libjson_c_la_LIBADD) \
+		-:HEADER_TARGET json-c \
+		-:HEADERS $(libjson_cinclude_HEADERS) \
 		-:PASSTHROUGH LOCAL_ARM_MODE:=arm \
 	> $@