You can use it safely if you pin their certificate. This adds complexity to the maintenance and deployment but it does actually improve security.
If you do not, then it depends on how they built their trust chain: if they are only using self-signed certificates, then you're out of luck and can't securely use their services. If they just use a private CA, you can still import their CA and trust it.
Overall, I would recommend you implement certificate (or root) pinning.
Edit @LieRyan made a good comment that I'd like to expend on.
In some configuration, pinning a certificate will require your to add it to the machine's root anchors lists. For instance, this is required if you're using IIS on Windows to host your application.
Now, depending on how the certificate was generated, this might be or might not be an issue. Specifically: if the certificate does have a "key usage" property and if that property does NOT list "Certificate Signing", then it can safely be used because it can't be used to sign other certificates (details are a bit more complex but that is the most important one).
If the certificate does NOT have a "key usage" property or if that property has "certificate signing", then it could potentially lead to other certificates signed by that cert to be trusted by the OS. If you implemented certificate pinning, that should not be an issue for your app (since pinning will prevent even otherwise valid certs to be used) but it might be for other part of the OS.