Hi Majaeit,
Messagebird provides a API you could try. You can test this API via a REST Call. I have good experience with this, well documented and perfect uptime.
In addition to the other answers, if you are just looking to send a message from a mobile device that is running your application, you can use the “Send Text Message” activity in Nanoflow Commons.
https://docs.mendix.com/appstore/modules/nanoflow-commons
there is a whole set of module is the marketplace which will help you to implement such
https://marketplace.mendix.com/link/component/116784
https://marketplace.mendix.com/link/component/109270
https://marketplace.mendix.com/link/component/109621
Didn’t use them myself yet, though I expect that when you know how to model a Mx app, these will be sufficient