PEPZ

The way I generally do it is set up a bot in node.js using steam-tradeoffer-manager, and create a Web server in that bot which accepts commands to send trade offers. Then use curl in php to command the bot to send an offer.
 
I believe there are php libraries for interacting with Steam, but I don't personally think php is well suited for that task.

Here's an idea. Three options for createOffer():
manager.createOffer(steamID); // create an offer without a token. you can set it later manager.createOffer(steamID, token); // create an offer with a token manager.createOffer(tradeURL); // automatically extract the SteamID and token from the trade URL