Just a couple of suggestions--for what they're worth...
1) You could try to borrow a 'have a heart' trap--those are spring loaded so
that when cat goes into cage & steps on bottom, the door closes.  Bait it
with something he really likes--tuna fish, i understand kfc is a big draw,
anything--particularly if it smells (which you can enhance by warming food a
little).  You might call your local shelter or any local rescue groups to
see if you can borrow one.

2) I had to trap one of the strays I was feeding--would let me pet him but
not be picked up or anything.  I bought a used smaller wire dog crate from
my local shelter for $10, (they told me people leave them when they
surrender animals).  I got him used to going into it to eat with me sitting
next to it.  When he got far enough into it, I swung the door QUICKLY!
First time I tried, I was so afraid of catching his tail, he got out.  I got
a little braver next time & though he really thrashed around in there, he
calmed down pretty quickly when I threw a towel over it.  I did not take him
out of it until we got to vets--but that's another story!

Good luck.  The fact that he lets you pet him is a big plus in your favor...