LCL CTLR ISSUES VECTORS AND ALT CHANGE TO ACR TO AVOID VFR XING TFC.

Narrative

I WAS WORKING THE ARR POS AT ZZZ APCH. I WAS WORKING A B727 INBOUND ON THE ZZZZZ2 ARR. HE WAS AT 10000 FT AND I DSNDED HIM TO 7000 FT AT THE NORMAL POINT. ABOUT 20 SECONDS LATER; I NOTICED A TARGET WITH A LIMITED NON DISCRETE DATA TAB (1200) WITH MODE C INDICATING 8300 FT. I THEN ISSUED ACFT X 9000 FT AND ISSUED VFR TFC. ACFT X DID NOT SEE THE TFC UNTIL IT WAS AT HIS 3 O'CLOCK POS AND APPROX 1 MI. I FORGOT TO MENTION I ALSO VECTORED ACFT X OFF THE ARR RTE TO AVOID OVERFLYING OVER THE UNVERIFIED TARGET. IN OUR ENVIRONMENT CLASS C AIRSPACE THE VFR ACFT WAS IN THE RIGHT TO BE WHERE HE WAS; BUT I FEEL IF HE WERE REQUIRED TO PARTICIPATE IN VFR ADVISORIES; THEN I WOULD HAVE KNOWN AND VERIFIED HIS ALT. AT THE TIME OF THE INCIDENT I WAS ONLY WORKING 2 ACFT. IF I HAD BEEN WORKING MODERATE TFC; I COULD HAVE NOT OBSERVED THE VFR AND THE 2 ACFT COULD HAVE GOTTEN CLOSER THAN THEY DID. THE X ACFT THAT FLY INTO ZZZ AREN'T PRESENTLY REQUIRED TO BE EQUIPPED WITH TCASII SO THE PLT HAD NO ASSISTANCE IN FINDING VFR'S EXCEPT FOR ATC. THIS TIME THE SYS WORKED; BUT IT COULD HAVE WORKED BETTER HAD I BEEN TALKING TO BOTH OF THEM.