You could use a u-bolt upside down like so:

Thanks @Seabornman Do I need to drill holes? I am trying to avoid drilling holes or any modifications to the railing.

Once I have the U-Bolt, would the screws be facing upwards or downwards or where will the platform feeder attach to the bolt? Sorry for asking newbie questions.

Also @Seabornman do you think the u-bolt will be able to handle narrow railing of width 1.5''?

You can buy u bolts in different widths. Just buy two that fit around your rail. Face the bolts up. If you don't want to drill through the feeder and have bolts sticking through, you could have a board or piece of exterior plywood that the ubolts attach to and then screw the feeder to that. You may have to either countersink the bolt heads and strap into the board, or drill come shallow holes into the feeder so it sits straight, or shim up the board so feeder sits straight. Here's a stainless steel u-bolt in the size you want:

You may have to cut the bolt ends off with a hacksaw afterwards if they're way too long.

This is perfect @Seabornman Much appreciated!