A better option is to use SASS to regenerate the btn-* CSS classes as desired using the appropriate SASS mixins...
Bootstrap 5 (update 2023)
Bootstrap 5 has the same button-variant and button-outline-variant SASS mixins which can be used to customize the button color after bootstrap is imported...
/* import the Bootstrap */
@import "bootstrap";
/* ------- customize primary button color -------- */   
$mynewcolor:#77cccc;
.btn-primary {
    @include button-variant($mynewcolor, darken($mynewcolor, 7.5%), darken($mynewcolor, 10%), lighten($mynewcolor,5%), lighten($mynewcolor, 10%), darken($mynewcolor,30%));
}
.btn-outline-primary {
    @include button-outline-variant($mynewcolor, #222222, lighten($mynewcolor,5%), $mynewcolor);
}
https://codeply.com/p/UNvB5hRsfF
Bootstrap 4 (update 2019)
Now that Bootstrap 4 uses SASS, you can easily change the primary button color using the button-variant mixins:
$mynewcolor:#77cccc;
.btn-primary {
    @include button-variant($mynewcolor, darken($mynewcolor, 7.5%), darken($mynewcolor, 10%), lighten($mynewcolor,5%), lighten($mynewcolor, 10%), darken($mynewcolor,30%));
}
    
.btn-outline-primary {
    @include button-outline-variant($mynewcolor, #222222, lighten($mynewcolor,5%), $mynewcolor);
}
https://codeply.com/p/JnV3xDDiaH (SASS demo)
This SASS compiles into the following CSS...
.btn-primary {
    color: #212529;
    background-color: #7cc;
    border-color: #5bc2c2
}
.btn-primary:hover {
    color: #212529;
    background-color: #52bebe;
    border-color: #8ad3d3
}
.btn-primary:focus,
.btn-primary.focus {
    box-shadow: 0 0 0 .2rem rgba(91, 194, 194, 0.5)
}
.btn-primary.disabled,
.btn-primary:disabled {
    color: #212529;
    background-color: #7cc;
    border-color: #5bc2c2
}
.btn-primary:not(:disabled):not(.disabled):active,
.btn-primary:not(:disabled):not(.disabled).active,
.show>.btn-primary.dropdown-toggle {
    color: #212529;
    background-color: #9cdada;
    border-color: #2e7c7c
}
.btn-primary:not(:disabled):not(.disabled):active:focus,
.btn-primary:not(:disabled):not(.disabled).active:focus,
.show>.btn-primary.dropdown-toggle:focus {
    box-shadow: 0 0 0 .2rem rgba(91, 194, 194, 0.5)
}
.btn-outline-primary {
    color: #7cc;
    background-color: transparent;
    background-image: none;
    border-color: #7cc
}
.btn-outline-primary:hover {
    color: #222;
    background-color: #8ad3d3;
    border-color: #7cc
}
.btn-outline-primary:focus,
.btn-outline-primary.focus {
    box-shadow: 0 0 0 .2rem rgba(119, 204, 204, 0.5)
}
.btn-outline-primary.disabled,
.btn-outline-primary:disabled {
    color: #7cc;
    background-color: transparent
}
.btn-outline-primary:not(:disabled):not(.disabled):active,
.btn-outline-primary:not(:disabled):not(.disabled).active,
.show>.btn-outline-primary.dropdown-toggle {
    color: #212529;
    background-color: #8ad3d3;
    border-color: #7cc
}
.btn-outline-primary:not(:disabled):not(.disabled):active:focus,
.btn-outline-primary:not(:disabled):not(.disabled).active:focus,
.show>.btn-outline-primary.dropdown-toggle:focus {
    box-shadow: 0 0 0 .2rem rgba(119, 204, 204, 0.5)
}
https://codeply.com/go/lD3tUE01lo (CSS demo)
To change the primary color for all classes see: Customizing Bootstrap CSS template and How to change the bootstrap primary color?