Focus on using the Hook Fighter feat
You don't need to rely on weapons with the grapple property. They are not a reliable way to grapple opponents since they only grapple on critical hits, and being piercing weapons mostly, they only crit on a 20.
The Hook Fighter feat opens up a lot of possibilities when using a Grappling Hook as a weapon, allowing you to use it as a reach, tripping or disarming weapon.
But Hamatula Strike would allow you to grapple the enemy without actually requiring the grapple quality or wasting a Standard Action to initiate a grapple, but it has heavy requirements (3 feats and BAB +7). It is also the only way to initiate grapples on manufactured weapon attacks, all other methods require natural attacks.
There are other weapons that serve a similar purpose as well, like the Chain Spear. The Kyotetsu Shoge is a dagger tied to the end of a long rope but is not exactly a chain. There's also methods to turn a Spiked Chain into a reach weapon, using Dance of Chains for instance.
However, considering the minimum level to get Hamatula Strike (9th), Id work with Hook Fighter at first and trip my opponents instead of grappling them. Otherwise, you will have to rely on critical hits with a grapple weapon or spend a Standard Action to initiate a grapple.
Also, keep in mind that Grappling is not exactly constricting. Constricting usually means they cannot take actions, and is defined as being Pinned instead. While Grappled they simply cannot move away from you. There are several feats that help with how quickly you can Pin an opponent (see Greater Grapple), just make sure it's the thing you really want, as weapons with grapple will not let you pin your enemies:
While you grapple the target with a grappling weapon, you can only move or damage the creature on your turn.
Of course, you could always design a new weapon by working the details with your GM. But other than designing a Kusarigama-ish weapon that deals piercing instead of slashing damage, I don't see any possible outcome that will help your eidolon.
Finally, what you describe is something similar to what the Blades of Binding does, which is a magical weapon. But there is one magic item that will automatically grapple a foe when you attack, the Steadfast Grapple, a magical grappling hook:
This iron grappling hook is attached to a 50-foot length of silk rope. When a steadfast grapple is thrown, it automatically hits and attaches to any targeted object or structure within range of its rope. Against creatures, the wielder must make attack rolls as normal. Once attached, a steadfast grapple can only be removed with a DC 30 Strength check, the command word, or magic such as dispel magic.
Note that the description of the item is rather poor (it was published in an old adventure), and it doesn't explicitly say you get to automatically grapple the target. However, I do believe that was the design intent, otherwise it would be no different from every other grappling hook against creatures and that part of the description would be redundant.