If you can make the application use a proxy, check Fiddler.
I used stunnel recently to do the same with an android application - used the dextojar suite to take the application apart, replace the https://game.server.com URL with a http://game.server.com URL in the .dex file, re-create the .dex checksum, re-create and sign the apk, install the apk.
Use this iptables entry on my router:
iptables -t nat -A PREROUTING -i eth0 -p tcp -s 192.168.178.100 -d game.server.com --dport 80 -j DNAT --to 192.168.2.2:80
where 192.168.178.100 is my android device, and 192.168.2.2 is where i run the stunnel. (Alternativeely, you can probably fiddle with the DNS entries/hosts file of your client to make game.server.com == 192.168.2.2)
Then, use this stunnel.conf:
client = yes
accept = 80
You could possibly use stunnel if you set up two tunnels if you can't patch the client - one stunnel https server to connect your client to, which forwards to an stunnel http server, which forwards to the real https server, but i've never done that.
The third possibilty is mitmproxy, which might be even closer to what you need. I gave up on getting it to work on my Centos 5 system, but if you have a newer linux, it might be the easiest way to get what you want.
stunnel. And what documentation you already browsed through.