By the rules, no...
By the rules, the only way you get skills and weapon/armor proficiencies are through your classes at character creation and through feats (and possibly through one or two themes and paragon paths). In-world the feat you invest to become proficient in a skill represents the time & effort spent to train it.
...and there's a reason for that.
Because of the rapidly scaling cost of magic items, unless such training costs as much as level 26+ magic items then epic-tier players will end up being trained in all skills and all weapons/armor, simply because it's so cheap for them to do.
Your DM can always change that, though.
There's really no harm in asking. My personal recommendation would be to try to convince your DM to let you acquire the skill by doing some sort of quest, or possibly as a boon (a special blessing from a deity that gives a bonus and that is received in place of a magic item). That would make acquiring free skills difficult enough to avoid the concerns listed above, but still make it possible for you to get the skill.