Is it a good idea to determine coordinates of object on images with regression algorithms?
It is possible to train a neural network to solve a regression problem.
See facial keypoints challenge
You should note that training a network for regression is harder then training towards a classification problem.
The network is more prone to unnormalised, different deviation values per feature, weight initialisation etc.
Try following the tutorial and then you'll have a better grasp on using ConvNets for regression.

Good luck!