Tertulia has been defined by many to be a gathering to have conversation over coffee. Sobremesa is the time spent after meals to enjoy conversation with friends and family. Sobremesa has also been used rarely as table-cloth. Both Spanish words seem to be synonymous with subtle differences. But what exactly is tertulias de sobremesa? Is there some major difference between sobremesa and tertulia?
It is really quite simple.
As you said "Tertulia has been defined by many to be a gathering to have conversation over coffee." and also "Sobremesa is the time spent after meals to enjoy conversation with friends and family"
So if after meals you gather with friends and family to have a conversation, then you are having a tertulia de sobremesa
Only to be precise Tertulia in general is a conversation so it really does not have to be over coffee but it would be a lot better if it is.
Sobremesa is also what you do or have after a meal. We in Colombia call the dessert "la sobremesa" because you have your dessert usually "after" your meal.
It is usual also in many countries that after the dessert you have coffee which creates a good environment for a conversation that can be called tertulia.
To add to DGaleano's excellent answer, in Spain there used to be many famous Tertulias that were held regularly at a café.
En España, tanto en el ámbito tanto cultural como en las tertulias populares, pueden enumerarse diversos tipos temáticos: políticas, taurinas, literarias, teatrales o de carácter general. Suelen estar coordinadas por un fundador o alrededor de un personaje famoso que asiste con regularidad y a veces llega a darles nombre (como les ocurriera a Ramón Gómez de la Serna, Cansinos Assens o Valle-Inclán). Aunque lo habitual es que se conozcan por el nombre del local que la aloja, por lo general un café, y aunque se de la circunstancia de que son varias tertulias las reunidas en ese local a horas distintas o en épocas diferentes.
The same article names a few cafés where famous tertulias were held: Café Novelty (Salamanca), café Alameda (Granada), café Suizo, Nuevo Café de Levante, café de Fornos, café del Gato Negro, Café del Prado, café Colonial, café y botillería de Pombo, café Granja El Henar, café Regina (Madrid), etc.