The first alternative I can think of is a variety of thick and wide, transparent packing tape. In my country they sell "Gorilla tape". It's really thicker than regular and you can get a roll that is 3 inches wide. I have not tried in that specific type of repair, but to protect a label I had made on a ceramic coffee cup and that piece of tape withstood frequent washing and microwaving no problem at all. (Actually the mug got broken due to a fall before the tape shown any damage). You would just need to clean and dry the plastic before applying the tape.
(Edit: For anyone not in the USA, like me, special tapes like the repair tape mentioned by @ChrisH may not be available locally, or may be not popularly known by that name. Here they some times sell specialty tapes, often unbranded or generic but due to similarity, they are located in the same aisle than regular packing tape. For example, clear, fiberglass reinforced tape is available, but you have to personally look for it, since the store clerk may not know it by name. The tape I mention is indeed way thicker than regular packing tape, it would be overkill unless your'e sealing a really big box with heavy contens.)
Second: Here it is very common to use a piece of transparent plastic on top of the table cloth in order to prevent food and beverage spills from staining it. It is sold in some hardware stores and plastic item stores. It is available In various thicknesses. You may be able to buy a yard of the material (for relatively cheap) and sew a whole new window. (replace the whole transparent piece by a new one). Sewn plastic can be rainproof for light rain, just use a needle that is thinner than the thread.
Another source for transparent (or not) plastic is a shower curtain or a rain cape. Those kind of items are easily available on supermarkets and "dollar stores". You may be able to get a color that even works better for you in terms of aesthetics/visibility. For example, if that where me, Id use a thick yellow raincoat.
Since you need a small piece of fabric, you may re use an old or damaged one.
A third option is the kind of patch that are sold for inflatable pools and pool toys. Those are light, flexible and usually come with a suitable adhesive. Since they are airtight when applied correctly, they should be waterproof. Such items can be bought cheaply when off season. I once patched the inflatable ring of a large pool that was later "abandoned" in the patio for somewhat longer than a year. The patch did resist very well even under tropical sun. It certainly lasted until the pool ruptured somewhere else.
