They're unicode characters rather than alt codes. The easiest way to enter them is to copy and paste.
You can enter them like alt codes but they require you to create a registry key under HKEY_CURRENT_USER of type REG_SZ called EnableHexNumpad, set its value to 1 then reboot. Please don't attempt this if you're unsure of what you're doing!
If you're using them for articles, you can use their HTML entities instead. You simply put the entity where you'd like the icon in the HTML editor.
Empty heart(♡): HTML entity: ♡ Alt entry: Alt +2661
Black heart(❤): HTML entity: ❤ Alt entry: Alt +2764
(note: entering them using Alt means you need to press the + key on your numpad which won't work unless you've added the registry key)
I also found this program while googling which will allow you to enter unicode characters without changing the registry. It seems fairly old, but it's simple enough that it should run on most Windows systems.