I thought maybe one of the experts would jump in here, but since they didn't I'm going to say you've got a really tough problem there because the issue is your pool is too low. It was installed too low to begin with and they got around it by installing the lipped coping. The pool should be elevated such that water runoff does not get in the pool even during a big downpour. Precast concrete can be made in just about any shape you can imagine, it shouldn't be a problem reproducing the original shape or creating a new one that is similar in shape. You might check with some better PBs in your area and price replacing just the coping.

They make these long bags you can buy and fill with water. They are pretty cheap...so cheap they only last about 1 season. They are actually used to hold winter covers down. You can try filling them up and placing them around the perimeter of your pool to act as a "dam" or "levee". Not are not going to be 100% but they are pretty cheap and perhaps if it was just a little better you could live with it. ??

The only other way I think you could fix it, is to cut in a ditch with a concrete saw all the way around the pool and install a french drain of sorts. That, of course, would be an expensive solution but would probably solve the problem.

BTW, I would fault the folks who replaced your coping and tile...there is no reason they could not have "built" up the coping a bit with more mortar and covered it with some sort of miniture tile look to get it above grade. Especially if the material they were replacing was thicker...which appears to be the case.

definitely the folks who replaced your coping did not help you out. barco is right, they easily could have built up the mortar a little bit to raise the lip...they have to play with the mortar levels all the time when they are installing flagstone coping or soe other natural stone with irregular depths.

but ultimately, the cause really rests with whoever installed your pool deck. your pool deck is supposed to have just the tiniest, most imperceptible "tilt" to it, so rainwater flows away from the pool. mine has this and you would never notice the tilt/slope when you look or stand on the deck, and we never get runoff into the pool. so if you are planning on replacing your pool deck in the near future, make sure they do this for you.

Thanks for the responses.
Yes, plaster company was a disgrace all around. If anyone in the Eastern PA, western NJ area want a recommendation who not to use - I have the worst here for you.

A few (just a few) of the many things they did wrong:

1. Prep for mortar bed to lay coping. None - they chipped any still tight old tiles away then left all the loose chips and dust on top of pool wall. they were ready to actually pour new mortar right on top of all the loose particles. I was livid when I saw it and went and got a broom myself and filled a bucket full with dust and chips before I was done sweeping. When I tried to express my concern about leaving the loose stuff - no speak english was the response - so I swept it myself. Got Boss on phone - my guys know what they are doing - was his response.
2. Coping was multicolored bricks for an alternating color pattern. they could not understand that and began laying aside the different color bricks thinking these were mixed in by error. By the time they got 3/4 around pool they had so many "mis-colored" bricks they must have realized the pattern and started mixing them in. well you can imagine the new color pattern of our coping bricks.

In any case the pool has origianl concrete decking which was good enough shape. Decking rests on pool wall on inside and floats on the dirt on outside edge. I assume this is called cantilever design. there is adequate slope on this deck to get runoff in most seasons however there is a retaining wall on 2 adjacent sides of pool area which prevents further runoff if heavy rain and flooding is excessive. In winter when the ground is frozen more water accumulates instead of running off. Hence the problem.

I guess our best solution is to install an actual drain pipe or grating drain along this area to divert water rather than have it filling up and overflowing into pool. Perhaps at the edge of decking and between patio area paving bricks and decking. Not sure though that the drain will not freeze also if very cold since it would just below the surface.
That is why I was considering some type of dam instead.