Average The Skills
If he has to use two skills, average the two skills together and then make one roll. In this case, that'd be a single roll to get 50 or below, since he has 50 in both skills (so the average is 50).
If he was better at one skill than another, it'd look slightly different. Say he has a 50 in Stonecarving and 25 in Artistry. That makes the average of them 37.5, so he'd have to get a 37 or below (or a 38, depending on how you want to round).
That basically treats it like he's using both skills and has to succeed on using them in combination, rather than having to succeed on separate rolls for both. It also keeps it to a single roll with similar odds, and is relatively simple to implement for players.
Alternative - Geometric Mean
The downside to averages is that if you're really good at one skill (say 100 in Stonecarving) and really bad at the other (0 in Artistry), you still have a 50 in the combined skill. That might not be what you had in mind, as someone with no artistic talent doesn't suddenly gain it just because they are working with stone.
In this case, an alternative method is to take the Geometric Mean. For two skills, that is this formula:
$$\sqrt{skill_1 \cdot skill_2}$$
So, if you have 100 in Stonecarving and 0 in Artistry, you do \$100 \cdot 0\$, which is 0. The square root of that is 0. As a result, you now need to at least have 1 skill point in Artistry in order to attempt the combined result. If you did have Artistry 1, you'd get \$100 \cdot 1 = 100\$, the square root of which is 10. As you add points in Artistry, your chances will quickly increase.
For my previous example of 50 and 25, you'd get \$50 \cdot 25 = 1250\$, the square root of which is 35.3.
The main downside to this method is that in a tabletop game, it's extremely hard to calculate without a calculator. Even with one, it requires a more complicated understanding of math and is more time consuming. If you put this in a rule book, there will be people who won't understand what you want them to do. For something like a video game where it's calculated by the software, that isn't a problem.
(Thanks to Peteris and Vatine for the suggestion!)
Alternative - Minimum/Maximum
A very simple method for combining skills is to use either the minimum skill in the two of them, or the maximum skill in the two of them. The maximum means you're just using the skill you're better at, while the minimum means you're using the skill you're worse at.
In the case of the minimum, it simulates the idea that you have to succeed on what you're weaker at in order to accomplish the goal. This lets you do it in a single roll, and is very easy to understand. It also has some issues, in that if you're extremely good at Stonecarving and so so at Artistry, your Stonecarving gets ignored in this system as you only roll on your lower one (Artistry).
Because of that, I don't think it really accomplishes what you intend very well, but it's ease of use is a significant upside over the other suggestions.
(Thanks to Neil Slater and Ellesedil for suggesting.)
Best Answer
Most uses of a d100 are for a DM
There are a lot of d100 random encounter tables on pages 92 - 112 in Xanathar’s Guide to Everything
There’s A framing event table in the DMG page 79, a dungeons location table page 99, there are d100 treasure tables pages 136 - 139; random magic item tables pages 144 - 149; several tables in the magic items section determining what the item’s effects are pages 135 - 213; tables for helping create sentient magic items pages 214 -217; tables for artefact properties pages 219 - 221; effects of madness pages 259 and 260; a number of tables on 293 - 301 for helping design dungeons
Mixing Potions
Page 140 of the DMG has a d100 table for a variant rule about mixing potions:
The table details what might happen if you start mixing multiple potions together. Effects range from them blowing up in your face, turning to poison, working normally or becoming permanent. The most likely result though is that both potions simply work normally.
Teleportation
The DM rolls on the table for Teleportation whenever the spell is cast to determine if you arrive at your intended destination successfully. Different methods of using Teleportation or different levels of information determine which specific table you roll on as there are several tables in one block.
However, there are some for players
The carousing table in the DMG page 128 and the running a business table page 129 are meant to expand on the downtime activities options for players.
There are also a number of tables for player backstories in XGtE pages 61 - 73. There are also tables for character names pages 175 - 192.
The sorcerer’s wild magic table page 104 is an obvious one for players that springs to mind.
Trinket tables, PHB 160 and 161. They say that can also be used by the DM to help stock a dungeon.
Divine intervention, PHB page 59, requires a cleric to roll percentile dice (or a d100) to see if their god intervenes:
Allowing players to roll on DM tables
(Note that this section requires the DM to be willing to allow players to roll on DM tables. It is not guaranteed nor expected that your DM will allow for this, this is simply a suggestion which would allow for players to roll a d100 more frequently.)
User Phlarx pointed out that, although many tables are intended for use by the DM, a DM may allow the player to physically roll the d100 as the DM reads the result on the table. From their comment below this answer:
From user Phlarx’s experience, allowing players to roll on tables intended for the DM, such as the treasure and item tables, has increased player engagement in their game.
From this we may infer that allowing players to roll on other tables intended for DM use - such as the Teleportation table, the Mixing Potions table, or tables which determine what effect a magic item has - could also increase player engagement.
The process of allowing players to roll on DM tables may look like this, the appropriate dice being a d100 in the case of this question:
“The DM either picks a result from the table or determines if a roll is needed. If a roll is needed, the DM asks the player(s) involved to roll the appropriate dice. The DM reads the result of the roll and checks it against the table, reading out the result on the table.”