You can use the EZAPI interface programs to manage the traffic natively in your COBOL programs or use one of the many variants of MSMQ to WebsphereMQ or JMS.
The EZAPI stuff will let you do the direct http puts, but you will need to manage it all.
Why not just hook the MSMQ into whatever queueing software you have on the mainframe and make it work the way it was intended?