There are dozens of such methods, as your problem is simply regression. Just google for such methods, this is really to broad to even list it here. Among other, you have:
- k-nn regression
- regression trees
- support vector regression
- ridge regression
- ...
Apart from other methods - remember, that even neural networks alone are very complex objects, with many parameters and formulas, so in order to get good results you need to spend much time on tuning them.