Hi, welcome!
A locking clip is the right tool... and can be very frustrating. So you're on the right track, hang in there. You're trying to install it on the outside, not the middle? If you have a lap-only belt in the middle it might be easier--there might be a locking latchplate if you have a lap-only belt (and the lap-only belt isn't safe for anyone else to sit in, so putting a car seat there is good).
Here's how I installed my MyRide behind the passenger seat in a 95 Civic, also without locking belts:
1. put car seat on the seat facing the rear of the car.
2. thread belt through and buckle.
3. Climb in car and stand behind the seat (put the front seat all the way up first). Push in to the back of the car with your tummy and down with your left hand.
4. tighten belt with your right hand, feeding the shoulder portion up to make the lap portion shorter and the seat tighter. I can't quite remember the MyRide's cover, if you can pull it back to see the belt path, do so.
5. When it's very tight, unbuckle seat belt but hold the belt together above the sliding latchplate. Fasten locking clip within 1" of the latch plate.
Now: the fun part! Getting it buckled again with the locking clip on! The key here is to push in and down, so I'm going to use anything I've got to do that. It might work to stand behind it like I did when tightening. It might work to lean in to it from the door. But what works best is having one person lean in and down like when tightening and one person buckling. I usually end up bouncing a bit, not too much (we don't want to break the seat), but giving it a bit of motion in the hopes that the belt will click in.
Hope that helps. Swearing is key for me. Feel free to tell that Toyota exactly what you think.