Looks to me like the relays are basically just switching pos and neg at the same time. Basically one is functioning in one polarity and the other is reversing the polarity to move the actuator the other way.
Just use two normal relays in place of each of the shown. Have one go to power and the other go to ground. Do the same thing with the other relay, just opposite.
Sorry I can't sit here and draw out a diagram for it right now, but if you don't get my drift reply to this and if i don't get to it in a while shoot me a PM to remind me and I'll try to get to it as soon as I can.
First thing you need to make sure the relays you have have 5 pins on them... many only have 4. In order for them to work properly in this situation you much have 5 pin relays.
I don't have time tonight to make a diagram.
Pin 85 - coil +
Pin 86 - coil -
Pin 30 - power or ground source (depending on what you need to switch
Pin 87a -connected to pin 30 when the coil is not charged
Pin 87 - connected to pin 30 when coil is charged