Thee are a couple of things you may be able to do.
1. You might be able to upgrade your Mac to Mavericks, then you could use the current version of iPhoto from the App Store.
You can use this link to see if your machine meets the requirements.
http://support.apple.com/kb/HT5842
You can find your Macs info by clicking on the Apple in the menu bar (upper left) select About This>More info mac here you can find the processor and memory, then click system report and you can find your model identifier, if it is Model Identifier Macmini 3,1 or later you should be ok to upgrade, (higher woud be the first digit being 3 or higher) You really want to have 4GB OF Memory(RAM) although Apple says Mavericks will run on 2GB.
2. The other alternative would be to get an older copy of iLife and install it on Lion.
http://www.amazon.com/Apple-MC623Z-A-iLife-VERSION/dp/B003XKRZES
The downloads i saw were sites I would not recommend, having the physical copy allows for reinstallantion if necesary.
Hope this helps
Make sure to run Software Update (Apple menu) so that you have 10.7.5 if the version is lower when you check About this Mac.