Can I use Center Ice in Costa Rica?
Firstly, I think Center Ice is strictly a TV based option for out of market within the US and potentially Canada for watching on dedicated channels, not streaming.
Secondly, internationally, it looks like a no for Costa Rica and in general all of Central America unless you already have a VPN and can mask your location into one of the eligible countries.
Eligible Countries:
NHL.TV
I've had it most years now since moving to Australia, but it seems to depend on your country's NHL broadcasting availability. If there is no NHL contract for broadcasting, then your country can get NHL.tv. Australia was on ESPN for a game of the week a few years ago and that prevented it from being on NHL.tv for those seasons which was demonstrably outrageous. I don't think there was a single opportunity to watch the Coyotes those seasons, and yet there was no legal option to pay for streaming.
I had a VPN two seasons ago when it was on ESPN+, but then this past season NHL.tv became available so I dropped it.
I think in your situation you might need to go with a VPN and then subscribe to either the national one or just get this new package. Maybe you can sell the game tickets or plan a trip.